There isn't really one key thing you can do to speed up the taming process, but there are a few things you really should do to make it easy on yourself.

   First of all, try to catch the pokemon you want with a Friendship Ball, if you didn't catch the pokemon in the wild, or if you hatched it from an egg then you'll have to start from scratch.

   Right away, give your pokemon an item to hold. You should try to give it an item that is useful for it. I suggest also using an item that doesn't go away (don't use berries), so you won't have to keep giving it things to hold if they use it up in battle.

   Try to use only the pokemon you're taming. Never let it faint or go into the red zone in battle. Heal it fully after every battle that causes it to go into the yellow or red zone. If your pokemon gets frozen, burned etc... heal it right away.

   The guide books tell you to feed your pokemon items like Carbos and Protien, but don't bother, it doesn't make a big enough difference to waste those items right now (those items are better used on higher level pokemon).

   Also, take your pokemon to the salon in Goldenrod (try to go there on days the older brother is there), or to 'Blue's' house in Kanto. You can keep track of your pokemon's tameness at the tame-rater lady's house (also in Goldenrod). Unless you really pamper it and avoid battles, it probably will not evolve until levels 25~30.

   If you take it to the salon every other third day, let it hold an item, and take it through all the trainer battles in Olivine (in the lighthouse too) and beyond... your Togepi will probably evolve into my favorite pokemon Togetic somewhere around level 30~35. Chansy is easier, it might evolve into Blissey for you around level 20~25 (if raised from an egg).

   Getting a Golbat to change into a Crobat is probably the toughest. First of all, it's not a very good pokemon, and it seems to not want to tame very fast. Take it to the salon a lot, and make sure it always has an item.

   If your in the mood for raising a Smoochum up to be a Jynx, make sure you don't let her evolve until she's learned the ever-popular 'Psychic' move (which Jynx cannot learn).