Allow the passive shield from Shield of Durand to refresh whenever possible as Galio has no other innate defence against magic damage, especially when it comes to ranged harass.
Charge Shield of Durand if you see incoming Crowd Control which you can't avoid. The channel won't be interrupted and the damage reduction will help you weather the assault until you can use your other abilities.
Shield of Durand slows enemies who get taunted which makes it more useful when peeling or running away.
Although monsters won't be taunted, Shield of Durand can still be used to tank their damage which may be worthwhile against Epic Monsters.
Even though Galio is focused at dealing with magic damage champions, he is not completely useless against physical damage champions. Many of them still deal some magic damage with their kits, and Galio can build armor. His Shield of Durand's active still reduces physical damage, even if the passive shield has little use against ADs. His amount of crowd control is also deadly against ADs too.
Still, picking an AD champion against Galio is by no means a bad idea. It forces him to start by building armor instead of building magic resistance which would make him scale better during the game. Also, ADs often have better tools to break through Galio's defenses.
To prevent Galio from using his Justice Punch to escape, try to stick to him. This way, Galio will stop at you and he will be unable to escape.
Be wary that with some AP, Winds of War is a very effective waveclear tool. Try to pick champions that can compete with his waveclear.
It is also a good way to harass the enemy, so building magic resistance is recommended, especially because all of Galio's offensive abilities deal magic damage.
Vel'Koz is one of the best mages to pick against Galio because of his Organic Deconstruction passive which allows him to do true damage, bypassing all magic resistance that Galio builds, in addition to bypassing the shield from Shield of Durand. In addition, Vel'Koz has high range and waveclear, two things that make him safe during the lane phase against Galio.