The Right "Intention"?
The intention or the motive behind any action is a core concept in Islam. The Prophet (SAW) told us that every action is judged according to its intention. This concept has far reaching consequences. If the intention behind any action is that we want to please Allah or to fulfill one of his commandments, then every such action becomes an act of worship and worthy of reward. By the same token, if the intention is to get praise from other people, to get any worldly benefit or any other selfish desire, then even the greatest act of charity or worship becomes completely wasted and can actually bring the displeasure and punishment of Allah.
For this reason, it is recommended to renew the intention in one's heart before any act of worship as it purifies the motive and also helps one to focus on the act.
It is sufficient to have the intention in one's thoughts. Speaking it out loudly is not recommended. Intention is connected to knowledge. If a person knows what he is doing then he has obviously made an intention.
See the video below for a discussion of the concept of intention by Yusuf Estes.