Check a good website like Lolalytics or something else to get an idea of the champion's item builds and runes.
Go into practice tool. Get a feel for each of the characters abilities. Learn how to CS with the champion (unless you are playing a support maybe).
Know which abilities to max first.
See how the damage trades off with a some AI that fits your lane in the practice tool. If you are a jungle, check to see how the clear feels to you. What camps you take, etc.
If it feels comfortable enough to use, go into Draft.
Play to win. Do not worry about what people say in chat if you do poorly.
If it feels like you are still not comfortable with the basics, maybe run through another practice session.
Do not rely on AI though. They are nearly useless. This is just to get an idea of how the abilities feel and how CSing (or clearing JG) feels.
Stay in Draft until you feel very confident on the champion in most match-ups for your lane (assuming you not already high elo and thus very good at the game in general, which you said you were relatively new?). If you get reasonably confident in a majority of matchups with the champion, go into ranked when you feel ready.
Otherwise, if people are flaming you, ignore it or let them know you are practicing the champion but you are still playing to win.
Key thing: Play to win, even if you start losing. Adjust your style to match what is happening in the game.
If you are getting trounced in lane, try not to feed and try to do other things to help your team win.
It helps a ton in these cases.
If you have even a single champion that you understand all of the matchups with, and you take each other champion into practice tool and run them through a time or two, you can get a good idea of how most matchups work and you can deal with a lot of situations better.
Keep in mind that Jayce is deceptively hard.
He seems easy sometimes but in reality, only a small handful of players are actually really good at him.
He is not really easy to get down to the point of being exceptional, so if you really want to learn a champion like that, do not get disheartened if you do not dominate in a few games, even if it seems your opponents are killing you with him every time.