In religious context, the word means 'sacred'.
It is also used as an meaningless intensifier, especially by older people in the UK. As you say, it indicates mild annoyance. For example, you might hear someone mutter, in an irritated fashion, 'Now, where did I put my blessed keys?'.
One point to note about pronunciation - this word is pronounced as two separate syllables /blesid/. This is one of a limited set of words where the past participle form and the adjectival form are written the same but pronounced differently.
The priest blessed the congregation ---> /blest/
'I'm so stupid. I make that same mistake every blessed time!' ---> /blesid/
How should you use it? Probably not at all. Unless you're talking about God, you have not reason to use it in the first sense. And seeing you are not an old-fashioned elderly British person, it would be very odd for you to use it in the second.
I hope that helps.