Can someone tell me some of the spells they mostly use in Harry Potter?

There are quite a lot of them! link you'll find a Список of them (from the Книги only, not the films) in alphabetical order :)

Expelliarmus, Expecto Patronum, Stupefy, Protego.

Expecto Patronum
Expelliarmus
Finite Incantatum
Flipendo    
Incendio
Legilimens    
Levicorpus
Lumos
Nox
Obliviate    
Petrificus Totalas
Protego
Reducto    
Reparo
Riddikulus
Sectumsempra
Stupefy    
Wingardium Leviosa

I think the spell most used is probably expelliarmus.