This is actually a very good question.
"Note" You should have the latest version of Java installed before trying this as you need that to play Minecraft.
For the client version
First you download and run your 'regular Minecraft' at least once. This ensures that your .minecraft folder has been made (if you don't know what that folder means, it's the folder where the game places most of its essential game files).
The next step would be to download Forge. You can download that here: FORGE.
You just select the right version you want and you run the installer.
Once you downloaded the file you right-click it and select the option to run it with Java.
Click install client and continue
Open the Minecraft launcher once done, make a new profile using the version with Forge- and the version you installed.
Play Minecraft.
For the server version
If you want to run your own server so your friends can join in on the fun, you would need to do some additional steps. The start is the same as the client version.
First you download and run your 'regular Minecraft' at least once. This ensures that your .minecraft folder has been made (if you don't know what that folder means, it's the folder where the game places most of its essential game files).
The next step would be to download Forge. You can download that here: FORGE.
You just select the right version you want and you run the installer.
Once you downloaded the file you right-click it and select the option to run it with Java.
Click install server and select your server folder.
In the folder rename the Forge-..___.jar to forge.jar
Make a new Text file and rename it start.bat (remove .txt)
In that file type:
java -jar forge.jar -Xmx1024M nogui
Run the start.bat file
To connect in game use the ip localhost.
For port forwarding, so other people can connect watch the VIDEO on how to install forge.
Now for the mods
Since you've now successfully installed forge you can start to install some of the mods. If you download a mod it usually comes in either a .Zip, .Rar or something like that. You don't need to extract this. Just keep it as it is.
So the first step would be to download the mod.
Next, go to your Minecraft folder, located at:
- Windows:
C:\Users\You\AppData\Roaming\.minecraft or %AppData%\.minecraft
- Linux:
~/.minecraft
- Mac:
~/Library/Application Support/minecraft
If you can't find the .minecraft folder you can do the following:
- Launch Minecraft.
- Select "Mods and Texture Packs"
- Select "Open Texture Pack folder"
- Go up one level
Now proceed to the .minecraft/mods folder (create it if it doesn't exist) and simply put your zipped/rarred/downloaded file there. (once again don't extract it just place it there as you downloaded it.)
Now if you run you Minecraft, select the forge profile you made, and create a world, your mod should be just there waiting for you to be explored.
Source : http://www.minecraftforum.net/topic/1900774-164-how-to-install-minecraft-forge-client-and-server-port-forwarding-tutorial/
Source: Where is my Minecraft folder on Windows?
Best Answer
A ZIP file is a file that has basically been compressed for the sake of storage or transmission. If you want to be able to locate the ZIP file, then look for the file within your mod that ends with ".zip". If you do not see that (it has most likely been renamed or put into another file already in the mod) then look for the file that has the image of a file with a zipper down it. I dont have that much experience with mods, but, like downloading a map (you would have to drag the maps zip file to the .minecraft saves file), I am guessing you just drag the mod's zip file into your .minecraft mods file. Hope this helps.