This isn't a big deal anymore. You can buy complete assemblys from most building supply places. Just be sure you shut the water supply line off first. That's the little pipe leading into the bottom of the tank. It usually has an on-off valve on it. If you want to replace that line too,you have to shut the water off further down the line. At the top of that pipe there will be a nut(usually 5/8,11/16 or 3/4)that will require a wrench to loosen. Turn counter-clockwise to loosen,clockwise to tighten. Now flush the toilet and empty the tank or you're gonna get wet!!
On the bottom of the tank again you will see a larger nut which holds the assembly in place. A pair of slip-joint pliers will do for this. Remove the nut and lift the assembly out of the tank. Dry and clean the area around the hole..dirt here will make a leak. Now simply set the new assembly in place,making sure the supplied gasket is between the new assembly and the tank surface. Reach under the tank and start the new nut onto the threads;be careful here..the threads are plastic and easy to strip. Once the nut is started well tighten it up SNUG..don't get rugged with it. That should have the assembly firmly in place. Now you hook up the supply line again..careful of the threads again. When everything's tight pour some water in the tank to check for leaks. Now GENTLY turn on the tap on your supply line and look for leaks again. Tighten nuts as required. You should be ready to fill the tank and make sure the float is working right. If everything's ok..give yourself a treat,you have just become HANDY!!!
BTW.. you can upgrade the assembly doing this..I put in one with a built-in float and did away with that rotton arm.