Blender is available both as binary executables and as source code on the Foundation site (http://www.blender.org/). From the main page look for the 'Download' section.
The Binary distributions comes in 6 basic flavours:
The Linux flavour comes actually in 4 different sub-flavours, for Intel and PowerPC architectures, with statically linked libraries or for dynamic loading libraries.
The difference between the dynamic and the static flavour is important. The static build has the OpenGL libraries compiled in. This makes Blender running at your system without using hardware accelerated graphics. Use the static version to check if Blender runs fine when the dynamic version fails! OpenGL is used in Blender for all drawing, including menus and buttons. This dependency makes a proper and compliant OpenGL installation at your system a requirement. Not all 3D card manufacturors provide such compliancy, especially cheaper cards aimed at the gaming market.
Of course since renderings are made by Blender rendering engine in core memory and by the main CPU of your machine a graphic card with hardware acceleration makes no difference at rendering time.
Download the file blender-#.##-windows.exe, being #.## the version number, from the downloads section of the Blender Website. Start the installation by double-clicking the file. This presents you with some questions, for which the defaults should be ok. After setup is complete, you can start Blender right away, or use the entry in the Start menu.
Download the file blender-#.##-windows.exe from the downloads section of the Blender Website. Choose to download it (if prompted), select a location and click "Save". Then navigate with explorer to the location you saved the file in and double-click it to start the installation.
The first dialog presents you the license. You are expected to accept it if you want the installation to go any further. After accepting the license,select the components you wish to install (there is just one, Blender) and the additional actions you want to take. There are three: Add a shortcut to the Stat menu, Add Blender's icon to desktop, associate .blend files with Blender. By default it is all checked. If you don't want some action to be taken simply uncheck it. When done, click on Next.
Select a place to install the files to (the default should do well), and click Next to install Blender. Press Close when installation is over.
Afterwards you will be asked whether you want to start Blender immediately. Blender is now installed and can be started by means of the Start menu (an entry named "Blender Foundation" has been created by the setup routine) or by double-clicking a Blender file (*.blend).
THIS MUST BE REWRITTEN FOR 2.28 BY SOMEONE WITH A MAC ACCORDINGLY TO THE WINDOWS STYLE
Download the file blender-publisher-2.25-mac-osx-10.1.zip from the downloads section of the Blender Website. Extract it by double-clicking the file, if it does not automatically extract as it downloads. Open the folder blender-publisher-2.25-mac-osx-10.1 and double-click the blenderpublisher icon to start it. Drag the blenderpublisher icon to the Dock to make an alias there.
Blender Publisher is available from the Blender Web site (http://www.blender.org/) in source form, and as a binary for Mac OSX. Unless you have problems running the binary, you will not need to download and compile the sources. From the downloads page, choose the "NaN Blender Publisher 2.25" link. Next, select the "Blender executables" link. You will not need a Publisher Key file for OS X.
Download the file blender-publisher-2.25-mac-osx-10.1.zip from the downloads section of the Blender Website. If you use Internet Explorer, the file will download and be automatically extracted with Stuffit(R) (http://www.stuffit.com/) to a folder on your Desktop named blender-publisher-2.25-mac-osx-10.1. If you use Netscape, you will be prompted to choose whether to download the file or have it automatically extracted with Stuffit(R). If you choose to have Stuffit(R) extract it, it will be extracted to a folder on your Desktop named blender-publisher-2.25-mac-osx-10.1. If you choose to download it, select a location and click "Save". Then navigate to the location you saved the file in and double-click it to have Stuffit(R) open it in that location. It will extract the files to a folder named blender-publisher-2.25-mac-osx-10.1.
Open the blender-publisher-2.25-mac-osx-10.1 folder, and double-click the blenderpublisher icon to run Blender. You can also open your hard drive (the Macintosh HD icon on your Desktop), and open your Applications, then drag the blenderpublisher icon from the original folder to the Applications folder. If you wish to leave the original blenderpublisher file and make a copy in the Applications folder, hold the option key while dragging. If you wish to make an alias to the original blenderpublisher program, hold both the option and command keys while dragging the icon.
You can also place the binary, a copy of the binary or an alias to the binary on your Desktop instead of the Applications folder, or put an alias on your Dock simply by dragging the program icon down to the Dock.
Download the file blender-#.##-linux-glibc#.#.#-ARCH.tar.gz from the downloads section of the Blender Website. Here #.## is Blender version, #.#.# is glibc version and ARCH is the machine architecture, either i386 or powerpc. You should get the one matching your system, remember the choiche between static and dynamic builds.
Unpack the archive to a location of your choice. This will create a directory named blender-#.##-linux-glibc#.#.#-ARCH, in which you will find the blender binary.
To start blender just open a shell and execute ./blender, of course when running X.
Download the file blender-#.##-linux-glibc#.#.#-ARCH.tar.gz from the downloads section of the Blender Website. Choose to download it (if prompted), select a location and click "Save". Then navigate to the location you wish blender to install to (e.g. /usr/local/) and unpack the archive (with tar xzf /path/to/blender-#.##-linux-glibc#.#.#-ARCH.tar.gz). If you like, you can rename the resulting directory from blender-#.##-linux-glibc#.#.#-ARCH to something shorter, e.g. just blender.
Blender is now installed and can be started on the command line by entering cd /path/to/blenderpublisher followed by pressing the enter key in a shell. If you are using KDE or Gnome you can start Blender using your filemanager of choice by navigating to the Blender executable and (double-) clicking on it.
If you are using the Sawfish window manager, you might want to add a line like ("Blender" (system "blender &")) to your .sawfish/rc file.
To add program icons for Blender in KDE
Select the "Menu Editor" from the System submenu of the K menu.
Select the submenu labeled "Graphics" in the menu list.
Click the "New Item" button. A dialog box will appear that prompts you to create a name. Create and type in a suitable name and click "OK". "Blender" or "Blender #.##" would be logical choices, but this does not affect the functionality of the program.
You will be returned to the menu list, and the Graphics submenu will expand, with your new entry highlighted. In the right section, make sure the following fields are filled in: "Name", "Comment", "Command", "Type" and "Work Path".
The "Name" field should already be filled in, but you can change it here at any time.
Fill the "Comment" field. This is where you define the tag that appears when you roll over the icon.
Click the folder icon at the end of the "Command" field to browse to the blenderpublisher program icon. Select the program icon and click "OK" to return to the Menu Editor.
The "Type" should be "Application".
The "Work Path" should be the same as the "Command", with the program name left off. For example, if the "Command" field reads /home/user/blender-publisher-#.##-linux-glibc#.#.#-ARCH/blender, the "Work Path" would be /home/user/blender-publisher-#.##-linux-glibc#.#.#-ARCH/.
Click "Apply" and close out of the Menu Editor.
To add a link to Blender on the KPanel, right-click on a blank spot on the KPanel, then hover over "Add", then "Button", then "Graphics", and select "Blender" (or whatever you named the menu item in step 3). Alternately, you can navigate through the "Configure Panel" submenu from the K menu, to "Add", "Button", "Graphics", "Blender".
To add a Desktop icon for Blender, open Konquerer (found on the Panel by default, or in the "System" submenu of the K menu) and navigate to the blenderpublisher program icon where you first unzipped it. Click and hold the program icon, and drag it from Konquerer to a blank spot on your Desktop. You will be prompted to Copy Here, Move Here or Link Here, choose Link Here.
To add program icons for Blender in GNOME
Select "Edit menus" from the Panel submenu of the GNOME menu.
Select the "Graphics" submenu, and click the "New Item" button.
In the right pane, fill in the "Name:", "Comment:" and "Command:" fields. Fill the "Name:" field with the program name, for example "Blender". You can name this whatever you'd like, this is what appears in the menu, but does not affect the functionality of the program. Fill the "Comment:" field with a descriptive comment. This is what is shown on the tooltips popups. Fill the "Command:" field with the full path of the blenderpublisher program item, for example, /home/user/blender-publisher-#.##-linux-glibc#.#.#-ARCH/blender
Click the "No Icon" button to choose an icon. There may or may not be an icon for Blender in your default location. You can make one, or look for the icon that goes with KDE. This should be /opt/kde/share/icons/hicolor/48x48/apps/blender.png. If your installation directory is different, you can search for it using this command in a Terminal or Console: find / -name "blender.png" -print
Click the "Save" button and close the Menu Editor.
To add a Panel icon, right-click a blank area of the Panel, then select "Programs", then "Graphics", then "Blender". Alternatively, you could click the GNOME menu, then select "Panel", then "Add to panel", then "Launcher from menu", then "Graphics", and "Blender".
To add a Desktop icon for Blender, open Nautilus (double-click the Home icon in the upper-left corner of your Desktop, or click the GNOME menu, then "Programs", then "Applications", and "Nautilus"). Navigate to the folder which contains the blenderpublisher program icon. Right-click the icon, and drag it to the Desktop. A menu will appear asking to Copy Here, Move Here, Link Here or Cancel. Select Link Here.
Download the file blender-#.##-freebsd-#.#-i386.tar.gz from the downloads section of the Blender Website. Here #.## is Blender version, #.# is FreeBSD version and i386 is the machine architecture.
Download the file blender-#.##-irix-#.#-mips.tar.gz from the downloads section of the Blender Website. Here #.## is Blender version, #.# is Irix version and mips is the machine architecture.
Download the file blender-#.##-freebsd-#.#-sparc.tar.gz from the downloads section of the Blender Website. Here #.## is Blender version, #.# is Solaris version and sparc is the machine architecture.