HELP With london underground+Places to visit?

Im going to see my girlfriend on new year for the first time, However i have NO idea how to get around the london underground. Ive been once before but luckily i was with my friend when we went to a concert and i couldnt work it out. Can anybody please explain to me how it works because i look at the map and just drool. Also, can anybody recommend any good places to visit or dine out in london or good spots to watch the fireworks without being crammed into a crowd? Romanticcccc ;D THANKS :)