Trading can be fun. You have to trade within your games generation. So, Diamond, Pearl, Platinum, and Soul Silver/Heart Gold can trade with eachother. Black and White can trade with eachother etc. You can transfer from an older generation to a new one on your own games but you can't go backwards. I have a few pokemon on Black that have been around since Ruby/Sapphire. What is funny is their original location becomes ...from a distant land ...or something like that. In order to trade/battle lets say with another person with Pokemon Black and White you will need their friendship code. You need to punch it in on the pal pad. Here is a video on how to do it (not my vid and he has a Japanese version of the game but its the same procedure)
http://www.youtube.com/watch?v=3mH8S8md5jY
Once your have that person on your friend code list you can meet them in the battle area (one of the ladies upstairs in the pokemon center). Its kind of weird but it does work. You can't communicate with them very well apart from in game stuff.
Egg moves come from the father your pokemon breeds with. For example, I have a Charizard that uses attack moves and I support them with the move Dragon Dance (ups attack and speed). Dragon Dance is usually not a move available on Charizard, so you need to breed dragon dance onto a male with a dragon type that has it and then breed for better stats once you have a decent daddy Charizard with dragon dance. It can take a while but once you have a few good pokemon to breed with you can get really good pokemon really quickly.
When you look at your pokemon they'll have a nature/personality, Quirky, Adamant etc. That attribute actually influences your stats (either raising one stat and lowering another, or being totally neutral). With every pokemon and moveset you'll have some ideal personality to support it. For example, Adamant will raise your attack and lower your special attack. So, that's great for a pokemon like Machamp who doesn't care about special attack but wants the highest attack possible. On top of that each stat can have a base value of 0-31. When you take your pokemon to a pokemon rater (he's in the battle subway) and he tells you "your pokemon is outstanding" that means all of your values are very high. He will also tell you what your best stats are. If he tells you your strength "can't be better" you know with 100% certainty it is a perfect 31. He has different messages depending on how good/bad your stats are (decent is the worst...he never says OMG that pokemon is terrible...but if you see decent that is what he means) You can also check/estimate those values with an online stat checker like...
http://www.serebii.net/games/iv-calcdp.shtml
Once you have a good pokemon you have to train its stats by battling it. When you fight and win you will earn effort points that influence your stats. There is a limit to the amount of points you can accumulate total and to each stat. You can typically only max out two stats or spread out your stats evenly (whatever your strategy is)
http://pokemondb.net/ev/all
I use that web site to figure out what I need to fight once I'm actually trying to train my pokemon. Usually I just play the game through with my set team and use berries to get rid of all of the points in stats I do not want. For machamp, as an example, I would make sure I have absolutely no points in speed or special attack.
http://www.pokefarm.com/berry-farming-the-ev-berries.html
If you have a decent dream world field, you can grow hundreds of berries easily. I don't bother doing this with every pokemon only those I want to use on a team since it is a lot of work.
Its quite complicated, but it is not something you NEED to do to have fun. Below are my two friendship codes if you want to add them. If anybody wants a decent pokemon I probably can breed you one really quickly and without cheating :).
