Is there a way I can battle random people on my DS? How? Please break it down to me as if I were 5 years old...

You mean battling other players at random, on Wi-Fi or whatever?

Yes... but only in Black and White, apparently.

so can you trade pokemone with someone you talk to online? or do u have to actually know someone irl who plays the game so that u can trade with them?

You can actually trade with people from anywhere in the world if you both have each other's Friend Code entered in each other's Pal-Pad & meet in the Wi-Fi Room on B1 of the Pokemon Center...

Locally though, you can use the 2F's Union Room as well as the above method, the Union Room doesn't require Friend Codes to be entered before hand but will prompt you to register the FCs of those you trade with in your Pal-Pad upon finishing in which you really should except as you don't have to actually remember the FC to do it & once entered, you can communicate for trade, battle, whatever via the Wi-Fi Room as well...

So for this you both need a working Wi-Fi Internet Connection(perferably an Internet Service Provider) & A DS System with a 4th Gen Pokemon Game, you know the DS ones & then;

1. Find the person you want to trade with regardless of how you know this person weither irl or via the internet...
2. Request & recieve his/her Friend Code, most likely from a message they send you with it typed in there somewhere & then give them yours by whatever method...
3. Enter the Friend Code in your Pal-Pad by first entering their Trainer name exactly as is(getting it the same way as the FC) followed by the FC you got from them...
4. Make sure you entered it correctly(duh)...
5. Schedule a time/date to trade & then both of you simply entered the Wi-Fi Room/Union Room(whatever) & you should see a sprite which should be them, just go to the computer & 1 of you request the other for trade & the other except...
6. PROFIT!...

Thank you so much for your post.