This tutorial is all about installing mods.
Most, if not all of the mods are client-side mods, meaning single-player only. Learning how to install Single Player mods will help in installing Multiplayer mods (below).
First, you need to download the mod itself. Go to the webpage with the mod on it, and find the link which leads to the download. If you can't find this, the mod is probably discontinued: you cannot use this mod anymore. Now, download the mod. For future reference it is better to keep the mod's description page open, so right click on the download link and click "open in new tab".
Next, you need to install the mod. This will be listed in a 3 step process:
- If you haven't already, locate your .minecraft file. For Windows 7/8, this is found in C:\Users\(your username)\AppData\Roaming\.minecraft; for Linux, this is found in your home folder; for all Macs, go to Library, Application Support, minecraft. Go to the versions folder in .minecraft, open the folder with the current version, and open the .jar file with the version name with WinRAR, 7zip or some other program akin to that.
- Some mods need other mods or programs in order to work, such as ModLoader. This is why it is best to keep the mod page open, because the installation instructions are listed. Download any and all of these mods, and open them in your zip program. In general, prerequisite mods are installed by copying all the files they contain into the minecraft.jar. After doing this, make sure to delete the META-INF folder in your minecraft.jar. This folder, in effect, prevents all mods from being installed.
- Now, open up the zip folder of the mod you wanted to install. If one of the prerequisite mods was not Minecraft Forge (more on this later), installation is again copying all the files from the mod folder into your minecraft.jar. If the mod requires Minecraft Forge, installation is even easier. Just copy the entire mod .zip folder (the one you likely downloaded) into a folder called "mods" in your .minecraft folder, not the bin folder. If it doesn't yet exist, just create the mods folder.
Finally, it's time to test your mod out! Run Minecraft. If you did everything right, then great! If you get the Minecraft crash screen, you probably didn't install the mod correctly, or, if you have more than one mod installed, you have incompatible mods. Refresh Minecraft, and install the mods again: if this problem still persists, look on the mod page for a list of incompatible mods, and instructions on how to fix them. Refresh Minecraft again and try installing the mods in a different order until you get it right. If you get a black screen, make sure you deleted the META-INF folder.
You're done! Have fun!
If you're still having trouble try this free guide. http://addictivearticle.com/2013/01/how-to-install-a-minecraft-mod/
Most server "mods" are Bukkit plugins and can easily be installed in your server folder.
Most non-Bukkit mods require a modified client to be able to connect to the server.