Select a wall mount that is strong enough to support your TV. Most 60 inch screens weigh in at around 150lbs, so you'll need a mount that supports at least that much, preferably more. Make sure that the mount is compatible with your specific TV. Consult your TV's documentation if you're not sure.
Turn on your stud detector and run it over the walls in the place where you wish to mount the TV. Find at least two studs near one another so that you can solidly anchor the wall mount.
Make a mark on your wall where each stud is located with your pencil.
Attach the first bracket to the back of your TV. You'll need to pry off the mounting hole caps on the back of the TV before you do this. This can be accomplished with a simple flat-blade screwdriver. The caps are round, flat pieces of plastic located on the back of your TV near the center.
Attach the wall bracket to the TV bracket, then measure the distance from the edge of the TV to the edge of the bracket. Once you have these numbers, determine where you want the bottom edge of the TV to go on the wall, then use your measuring tape to measure the appropriate distance so you know where the edge of the bracket will be located. Make a mark at this location.
Remove the bracket from the back of the TV and place it on the wall. Line it up with the mark you made in the previous step, then use your level to get the bracket leveled properly. Once this is done, make marks on the wall where each of the screw holes will be. Make sure the screw holes are all located over one of the studs you found in step two.
Drill the screw holes into the wall, then place the bracket over them to make sure they line up properly.
Ensure the bracket is level, then drive in the screws to secure it to the wall.
Attach the wall bracket to the back of the TV. Consult your wall mount's documentation on the exact method needed, as it will differ from bracket to bracket.