You will need forge for most mods out there. If they do not require forge, then they require Modloader. As for Optifine, It is not needed for any mods. Optifine however needs to be used for Texture packs.
I get that its a mod that adds an API for other mods, but what else does it do.
Forge is a mod API. It allows other mod authors to easily write mods that can be easily installed by dropping the zip in the mods folder instead of having to install them directly in the jar file. This helps mods be compatible with each other as they don't have to modify the game files directly. Forge does nothing in the game that you will see, it only allows other mods to function. A lot of mods nowadays need forge as they are written to use the changes that it has made to the base game. The install instructions will tell you if a mod needs forge or not. The other option is modloader, which is older but still used by a few mods. It's less functional than forge as I understand it (I'm not a mod author) but still capable and is the original (or nearly so) mod API for Minecraft. Forge includes an altered version of modloader that is mostly compatible with a lot of mods that would otherwise require modloader. It's best only to install one or the other, installing both modloader and forge is not a good thing to do. If a mod calls for modloader and does not work with forge, it can be reported to the forge team and they will try to make forge work with that mod in a future release.
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D_B To tell them how to live is to prevent them living.