Just like BINGO! Get enough cards for the kids in your Primary. I only have about 20 at a time, so I'll make about 25 cards. Here is the link I used to make my own SINGO sheets: Bingo Sheet Generator. It can randomly generate your cards so that no two are the same. I used image tags < src="whatever.gif"> instead of words to make picture SINGO cards since the little kids can't read.
Print out enough copies of these for 20, 30 or 40 kids and laminate them. I had visions of the kids getting excited singing some of the more fun songs and all of their chips sliding off, so I bought some repositional adhesive dots. I used a small punch to punch out circles from cardstock. This was just because I searched high and low but couldn't find those plastic bingo chips.
Either way, the repositional adhesive dots are a good idea. They were a buck each at the dollar store. Also print out larger single pictures that are on the SINGO cards, and put these into a bag. Each of these pictures represents a song.
In primary, hand out the cards as well as chips. Start by drawing a picture from the bag and play like regular bingo. Sing the songs that are related to the pictures. If a kid gets a line, they call out SINGO! And get to pick their favorite song.
Update: Camille sent in a quick note about a game of bingo she did. She had a real cage for little bingo balls and everthing. The bingo cards were premade and she used those for the big kids. For her little kids she drew a big bingo card on the board. If you don't want to make up your own bingo cards, this is the way to do it. You can probably assign a song to different numbers (or maybe sing the song with that page number?). Great idea, thanks Camille!