The only way out of a block string is to bara. If you mean a counter hit setup, which is usually a blockstring with a small gap after it followed by another attack, then you basically have 3 options.
1)Block. Really good option, only loses to grabs which generally aren't too bad. The more you block, the further your opponent gets which makes it harder to keep the pressure on.
2)Beat it out. A risky option but can turn the tempo of the match around. Most characters have at least one good special or ex that works against most counter hit setups, but it is character dependent. Shielding and dodging also serve this purpose.
3)Get away. Reset the match. This is usually done with a backdash or jump back midscreen, and with double jump to air dash in the corner. This option is much easier to stop while you're in the corner which is one of the reasons why you don't want to be there. Keep in mind that jumping has startup and good counter hit setups will hit you before you even get in the air. It's more useful after blocking some blockstring/counter hit setups and you've got some distance making tight pressure harder, but it still loses to most character's dash 5a, which is commonly used to reset pressure. Backdash is a better option most of the time but is still punishable if predicted and isn't available in the corner. These options rarely lead you to any damage, but sometimes you can gain initiative if you avoid the right move.
The first part is to recognize the counter hit setups in a string. These are the gaps between blockstrings where you have a chance to move, but not enough time to do much of anything. During this time you can do fast startup options(dp-type moves, shield/dodge, backdash), but slower ones will still lose. Generally after a few of these your opponent will be pushed further away and will try to close the distance, usually with a dash or iad. During this time you gain access to more options, like jumping away or sticking out a normal to either beat a dash or clash with an attack, but you need to know when this is coming because these options will always lose to a proper counter hit setup.