All I'd add to the previous comments is to show that you value them. There is one guy where I work who puts a lot of staff off with his abusive behaviour, both physical and verbal. I've found that I can relate to him well just by approaching him as a human being as opposed to a "patient", and respecting him enough to listen to what he's saying, asking for his input, etc. For a lot of people, being in residential care makes them feel angry, and the way some staff treat them makes matters worse (staff tend to be short with upset residents, which exacerbates the problem).
That man is in there because of physical care needs, not dementia, however. If it's dementia, all you can really do is talk softly and calmly, move at their pace, and encourage - don't force. And if they don't want to do something and are becoming agitated, simply walk away and document it. Remember not to take it personally.