here is my story.
I started to play ranked games so I wasn't good at begining, now I am 2x better, sometimes carry my team to win, but however I can't get rank up b/c:
1. Most common problem is ppl who do troll picks - ok you can leave w/o it starting, but you can't do it much only 2 times a day, so lets say it solved.
2. I am teamed up with totally newbies - this problem I can't get rid off. Its not even funny if your pick is last so you are support 80% and you go in lane with AD carry who doesn't even know what last hitting means. Its so unfair, I mean if I am lower rating shouldn't my teammates be for example higher rating and know how to play? I don't understand system of matchmaking at all...
3. Leavers. This problem is most painfull, I really don't understand why Riot allow ppl to leave games w/o getting strong penalty. I suggest 1 idea, if player leaves during the game and team lost he get all teams -rating total and rest get -0 (and he get +0 for win and still get -rating for leaving). When those leavers would actually stay on their rating, now its just sad to play when you know you have like 20% chance to win from begin.

Maybe someone can actually give some advices how to rank up or solve this problems.

p.s. I am really not bad player and I feel I can do much better than 1050 rating...

Congratulations, you just discovered your true elo.

I understand it is frustrating in the beginning especially if you get unlucky in your placement matches.

The best pieces of advice I can give you are:
1. Don't dodge! Try your hardest to win every game. Even if you have trolls in your game, you can still win! Team composition is not the most important thing in lower ELO.
2. Try to keep up the spirit in your team. If you see someone raging, either talk nicely to them and tell them what happened didn't matter, we can still win, or if they continue to behave badly, just ignore them and report them after game.
3. Think this way, you have four potential trolls or leavers or whatever, but your enemy team have 5! You should eventually gain ELO if you play good!

Just get better. Trolls? Leavers?? AFkers??? how come they are only in yer team bro? Enemy team got moar chances gettin baddies troll afkers than yer team. Get better and u 'll carry 'em. SoloQue represents your abillity of winning games, not doin' gud scores. Asumming your scores are gud indeed AND you know the game mechanics and how to react at every stage of the game (Earlygame, Midgame,Endgame). You should be able to climp teh ladder. Another guy who you absolutely trust can help with your goal by duo qeueing with you.

How to raise elo. First thing you need to stop careing bout your elo.

I had the same problem at 1200 for a while, kept getting trolls / leavers or just general bad players. Finally my bad luck ended and I got decent teams and jumped from 1200 to 1400 in a few days. Hopefully I will keep rising but we will see.

Just hang in there, eventually youll be teamed up with people that are decent enough.