You can win Trophies by playing Ranked matches. If you win a match you'll get some Trophies, if you lose you will lose some Trophies.
You will need to play some placement matches before you can claim your spot in the Ranked Season Leaderboard. The Season will last a few weeks (you can check how much time is left at the top left corner) and will award you some rewards for the league you ended the season in.
These rewards are awarded at the end of a season according to how you placed in the rank. Te emote is permanent, however, the frame will refresh after the next season ends and according to how you placed in it (you will also receive a new emote if you ranked in a different league).