I had that issue with: Ashe, Annie, Brand, Katarina, and Maokai.
Brand is a combo champ. You want to utilize his abilities all together as they add stun+damage/AoE to eachother depending on the order you use them in. Seperately they wont really be effective. Thus you probably have to wait for his abilities to be up before combo-ing again.
Annie, you want to keep an eye on her stun, and utilize that with combos aswell. With stun up, you can Q > R for massive damage to 1 champ or if you're in a team fight, you can W > R for massive AoE damage as youll stun everyone in range and destroy/kill them with summoning Tibbers.
Youd be surprised how well you can harass with her stun up, since most people who know annie, will keep that in mind and play it safe, makes for great ganking from your jungler too if they target your mid or lane. Shes become my fav AP champ :3