MultiMC has more functionality, it is easier to use. You do not have to do anything outside of the launcher as well.
To the OP, first create a new instance,
Click on the "Add a new instance" button as demonstrated in the picture. It should bring a smaller window that looks like this:
After that just double click it and it should download MC for you for that version. For demonstration purposes we're gonna install Forge.
To install Forge on MultiMC is probably the simplest process of all, as opposed to being the most difficult when doing it manually. First, with MultiMC open, you right-click on your instance as shown below:
When you right-click, a context menu will appear, which you click "Edit Mods" in. Once you click it, you'll be given the interface that makes installation a breeze, shown below:
The mod installing window has several tabs for the different types of installation methods. For Forge, we want to install to the minecraft.jar, so select the respective "Minecraft.jar" tab. While viewing this tab, you'll be given an extra button labeled "MCForge" for "Minecraft Forge" (the full name of Forge).
MultiMC has a built-in script that fetches Forge for you, and better, it only lists Forge versions that are aimed at your Minecraft version you have set for that Instance.
Click on the "MCForge" button to get a list as shown below:
Once you choose your Forge version to install, hit the OK button.
There's not much reason to check to see if it installed correctly, as MultiMC doesn't often make errors in this. That's it, you're done. Close the edit mods window, and double-click your instance to open the login screen. Login, and Minecraft Forge should be installed for you.
Right so we have Forge installed, and to make sure, just login, and it will display on the bottom left corner. Great, now we're gonna install a mod. For demonstration purposes, we're gonna install Biblocraft.
As Biblocraft needs to go in the mods folder, click on the Mods Folder tab, then press Add, find the mod zip, select it and press okay. Something like this should show.
Close, and attempt to run the game, if there are no crashes, then the game will proceed to the Menu with your mod installed. It is just that simple! But of course remember to check where the mod is supposed to go in, either Minecraft.jar, coremods folder, or the mods folder. Read the instructions!