Pride is to think oneself great and conceit is to be self-satisfied and impressed with oneself. The basis of all damnation is pride because it is the original sin of Iblees (Satan) and that’s why we have to be very wary of it. As for arrogance, the signs of it are to look down on people and reject what is true. That is why the sunnah of the Prophet, peace be upon him, is grounded in humility, both in outward actions and inward consciousness.
The best way to guard oneself against pride is to attribute all good in your life to Allah and praise Him for it. That stems from an understanding that you are a servant of Allah and every blessing you have is from Allah.