Often the key is prevention. Most squishy characters have some kind of ranged attack. Against Jax, for example, you should be pre-emptively lowering his health with occasional pot shots. If you have 100-200 more health than Jax, it usually means he simply won't attack you (or if he does, you can kill him!)

At the least, you can't let them just keep hitting you. If you ONLY run when Jax/Yi leaps at you and they get away without damage, they are winning the laning.

It depends a lot on who you are playing as, of course. Stuns/Blinds/Silence can hold many enemies at bay, and often damage them as well.

Positioning is key. Remember creeps do some decent damage early game and the enemy gets aggro when he targets you (he doesn't actually have to attack). In your specific example of jax, stay behind your melee creeps and if he comes at you, hit back! He can't take the damage from you and your minions early game unless you have let him do this several times unanswered and you are low. Be more careful than you think you need to be for now, until you are experienced at the small things.