to reach level 25 you need about 4860 experience. you gain experience after each game. 80 for 1st place, 30 for 2nd, 20 for 3rd, and 10 for 4th. you will also receive an extra 10 exp for completing the bonus goal stated at the beginning of the match. some of them are easy, and some are a bit more tricky. one actually requires spending silver coins, which is to send a gift to a friend, the cheapest costing 5. the total of those points is multiplied by your level bonus, which seems to be 5% for each 5 levels (rounded up to the nearest whole point). so levels 1-5 would get 5% extra exp, levels 6-10 get 10%. finally if you bought the +50% exp bonus before the match, that goes into effect last, giving you a final total for that game. it previously cost 40 coins, but is now at 75 coins per game.
the approximate experience needed for each level:
level-exp-(lv bonus)
5-500
6-670-(10%)
7-850
8-1020
9-1200
10-1390
11-1590-(15%)
12-1780
13-2000
14-2200
15-2420
16-2640-(20%)
17-2870
18-3090
19-3330
20-3560-
21-3820-(25%)
22-4050
23-4320
24-4580
25-4860