Want to learn how to dodge spells like a pro?

First of all, if you are taking damage, use perSona switch OFTEN. It removes all buffs, both positive and negative, but usually that's a good thing, and helps avoid all missile damage that you would be taking otherwise. So, for example, you walk up and that Sea Witch nova's you. Rather than reluctantly run away and have her shoot a good three arrows in the process, just instantly switch and run away as she shoots her first arrow. She'll not only miss her attack, but now since you're fast, she cant continually harass you.

If you arent in immediate danger, and you have a DoT on you (think Moonkin) then for gods sake SWITCH heroes! There's no use tanking damage for no reason.

Now, aside from that however, here are some general rules on how to dodge like a pro.
Here are the basic rules:
-- You can dodge anything that's a missile. If it's heading towards you and isn't an aimed projectile (like Shakti's spear, Sonic Shell, and Charged Bolt), then you can dodge it. This includes attacks from a tower. You have no idea how many times I've seen people die to a super long tower attack when they could've lived if they just switched.
-- Don't try dodging stuff that's AoE. If Ogre is about to shockwave you, DON'T SWITCH. You will take 2x the damage! That goes for a lot of stuff, like carrion swarm or even sonic shell.
-- Remember that perSona switch has a 6 second cooldown.

Now let's get into some specifics. Certain heroes out there have a nasty ability if they catch you right from your first switch. For example, Grove Guardian with a timely Entangling Roots will completely decimate a newly switched hero. Alternatively, a poorly timed Roots will do absolutely nothing (since you can simply switch out of it and never worry about it again). Usually in a situation, I like to gauge who has the most devastating disable, and what I can do to mentally prepare myself for the worst.

For example, I see a Blood Knight and a Grove Guardian chasing me. The Blood Knight goes to stun, so what do I do? I DO NOT switch. I tank the stun because even though it hurts, the disable itself is not so bad. I'm more worried about the entangling roots. So if I get stunned by the FireBolt, no big deal. Now the Grove Guardian thinks "Awesome, he's stunned! lemme follow up with an entangling roots!" The second he roots, I switch heroes. Because that's a huge "gtfo" in my book. Now they have to switch and recover from their cast animations and keep with your pace. Suppose the Grove Guardian DOESNT entangle you -- well then don't switch! Keep running.

Also you don't always just get perSona switch to save your back. ALOT of heroes have additional escapes that range from magic immunity to blinks and wind walks. It's important to chain these together effectively so you can get the most out of your escapes together. For example, if I was a BladeMaster in this situation, I would still tank the BK stun. But if the GG went to roots me, I could just Blade Fury out of it. And then if they switched heroes for a fresh new set of heroes, I would still have perSona switch ready to go.

Alternatively, you have to be able to see certain combos that could chain up on the one crucial disable. For example, you got a Thor and a Cerauno hot on your tail. The Thor manages to throw a stun at you. You better swap perSonas. If you don't, that cerauno will catch you with his Telekinesis, and then god knows what. The last thing you want happening is getting chained to oblivion. This is why a spell like Hex, Shakti's ult, can be so devastating. It can spell a sure death on a well-positioned gank because you simply can't "dodge" a hex.

Practice does make perfect but keep these things in mind from now on and hopefully you will be able to get away more often than not.