How do I level up my champion?

I completely don't understand how experience in this game works. I obviously try to last hit minions, if I can't I stay close to them to gain exp. I don't even roam much, unless I'm a support and need to deep ward. And I'm **always** behind in levels to my lane opponent. And I do mean always. At best, we're even. I had a game where I was 2/2, the enemy laner was 2/6 (which meant they were essentially afk for like a minute or two) and... they were 1 level ahead of me. Last game the enemy jungler basically made it 2v1 in the top lane for the first few minutes, so naturally he should steal some exp from the enemy toplaner. Despite that I was behind 2 levels behind all the time (partially because I died once, but does dying one time put you so much behind?). So how do I prevent that? And if I can't, how do I catch up? Because once I'm behind, I stay behind no matter what I do. It almost seems like advancing e.g. from level 10 to 11 is easier for my opponents than for me it is to get from 8 to 9.
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