NOTE: this is designed to help with WINDOWS, not MAC, or LINUX.
ANOTHER NOTE: This is how I install mods, and it works beautifully. most of the time...
STEP 1: Download and install 7zip
STEP 2: Download the desired mod
STEP 3: Download and run Minecraft once. then close out (mods are ineffective in browser)
STEP 4: Go to your computer's search method (several systems have different methods)
STEP 5: Search (WITH the %) %appdata%
STEP 6: Click Roaming
STEP 7: Click .minecraft
STEP 8: Click bin
STEP 9: RIGHT click minecraft (some sysetems will say minecraft.jar)
STEP 10: Open it using 7zip File Manager
STEP 11: DELETE META-INF (The GOLDEN rule of modding your minecraft!)
STEP 12: Open the mod, also using 7zip
STEP 13: Copy the files in the mod, to the minecraft.jar *
STEP 14: Close both the mod's window, and the minecraft.jar's window.
STEP 15: open and run minecraft.
STEP 16A: if when you log in, you get a black screen, close minecraft, DELETE your .minecraft folder, then return to STEP 3.
STEP 16B: if your minecraft starts normally, test one of the mod's functions.
STEP 17: If the mod's function works, you are set, read the warnings below! if it doesn't, DELETE META-INF!
*Use of mods in multiplayer without said permission is a bannable offence in almost EVERY server.
*Be careful what mods you download! some of them may contain a virus. (see others' comments on it's page to help you decide wether to trust it or not)
*Mods that add blocks/mobs to the game will use a Block ID. if 2 mods use the same ID, minecraft will put a brief crash report, then close.
*MANY mods are more complicated than this, but this will teach you the basics.
*if a file in the mod's folder has the same name as one in the minecraft.jar, put the contents of the folder into the matching one in the minecraft.jar
*never delete a file (exept META-INF) unless told to by the mod.
*if you mess up, do not attempt to fix it. delete .minecraft, then run it again. it will fix itself. (back to the most recent vanilla)
*VANILLA = UNMODDED minecraft
*DELETE META-INF. DELETE META-INF. DELETE META-INF. DELETE META-INF.
*if a mod's file has a README... READ IT!