The pattern that I prefer to use for "getting the key in your head" is to sing 1-3-5-1(high)-5-3-1-5(low)-1-7(low)-1. Adding the 7 and the lower 5 helps, but just 1-3-5-3-1 should do fine if you want simplicity.
"1" is *usually* the note the song starts on, but not every single time. To find "1", look at the beginning and ending notes of the piece, and try to find notes that are emphasized a lot. "1" will always sound like it has the least tension--all the other notes in the piece will feel like they should lead to "1". You can also get an idea from the key signature, although this can be deceptive, especially in medieval music.
Let me know if any of this doesn't make sense... :D