1. Hex Editing 2. Some Games Have A Editor For It (E.G Pokemon, NSMB) 3. Get A Hackers Help 4. Learn C++ And Make Your Own Game
Frankly your question is lacking of information. Each game has different file extension so the method of editing might differ from one to the other. Editing dialogs in a game such as Pokemon games on the NDS for example can be achieve through using a combination of NitroExploder and PPTXT. Some games ending in .ntft/.ntfp require the use of CrystalTile2, others uses Hex Editor, Summon Night uses SummonTransX combined with a text editor, others require you to use custom tailored programs such as DSLazy, etc. But basically you need to know how to open and edit the content of the game file as each file extension require different tool to access. If you want to taste how NDS rom translation project is like, go over to the TUTORIAL Section and look it up there.
I am curious in getting a hacker's help while simultaneously learning. I have a re-vamp project for Mario Kart DS in mind. Adds characters, changes the carts available by adding and removing and adds some GBA, N64, Gamecube and Wii Tracks that should've been added (especially after the Wii release with the potential for downloadable content) and a little something called All Cup Tour. Problem is I dunno game coding but figured if a hacker could help I could learn by doing.
That is a huge undertaking, and well beyond the basics of just replacing text/graphics. Even good rom hackers, modders, and programmers would struggle with it, if they could even do it, and would take some time. You aren't merely modifying a game, you are pretty much creating a new game.