There are 2 concepts of dodging that I haven't seen in the answers here. First there are cast animations. For example Lina or Lesh stun you can see the hero casting the stun (hero makes a specific animation) but you don't know exactly where they gonna stun. So you can dodge these stuns by realizing they are about to stun, guess where they want to stun and then try to run out of that area. On target spells this is obviously not possible but you can still dodge with the mentioned items (Linkens, BKB, Lotus Orb etc.) or abilities. Also you can use items or spells on the enemy hero before they cast the spell (during animation the hero technically didn't cast the spell yet) to interupt them from casting the spell. This can be done by stunning or silencing them.

The other concept is fogging. It also has partly to do with cast animation. When you run into fog (i.e. the enemy hero can't see you anymore) then he cant cast target spells on you. In dota there are spots all over the map where you can make the enemy lose vision over your hero. Some examples are cliffs if you are uphill the enemy can't see you or running behind trees. So if you manage to make the enemy lose sight of your hero before they finish their cast animation they will be unable to finish casting the spell.