Instructions
Sell any TMs that you do not need or want; you can only sell TMs, not HMs as they are much more valuable and only one of each exists per game. Head to the nearest Pokemart and talk to someone at the register. TMs range in value from $500 to $1500; this will make room in your bag and put more money in your pocket.
Go to a Pokemon Center and access your box on the PC. You can use this box to store items you may want to use later. You can drop off as many TMs and HMs as you want, and can come back for them if one of your Pokemon needs to know a certain move.
Access your bag's TMs and HMs section. Scroll through the TMs and determine if there are any you do not want to have, then select the TM and choose the "Toss" option to get rid of it. HMs cannot be tossed out because of their value to your overall mission in the game.