Most players will jump up, so charge the S and pop them when they come back down. If they jump out of range, hit G to cancel. If you want to save your white meter, charge S and hit G immediately to cancel. Clair has great wake-up games. Push H to add on a mid-air spin kick.
L is another way to counter wake-up attacks, but it's less fun.
If your opponent is down and you charge up the S just outside of their wake-up attack range, they'll normally freeze. If they try and roll away, released the S for an easy hit. Clair's basic middles include the basic M and running M. Try and stick with the running M because it cannot be interrupted and leaves you less exposed when blocked. If it's a counter add the H for an air combo. You don't have to input H right away, so only stick it on if you see your opponent go flying into the air.