That's right, sorry, forgot to mention the warm water on a Q-tip. Also, you'll want to use a damp Q-tip to clean its mouth, too, it can be VERY messy, if you don't make the milk the right consistency, it can be very sticky, stick all over them, and be very difficult to clean off. First time I did it I make it way too sticky, and had to feel dried milk flakes from Farble's mouth,
I was so afraid I was going to hurt him because some of them stuck on pretty tight. Which is why I say you're going to want to make sure it's more runny, and less sticky.
Oh, also, do not feed the baby on its back. I can include a video of how I held the first baby mouse I found for feeding...let me find it....
(that was the first one I ever found, his name was Farble for "Furry Marble" he was so tiny)
I wound up having to try different holding positions - he struggled endlessly for this one, but he was so tiny there wasn't really any other options to feed him in any other position. When I fed Muse, as he was older and more sturdy on his feet, I cupped my entire hand around him with his head poking out again my curled index finger and resting against the webbing of my thumb, and inside my fist I had my middle finger and ring finger supporting his butt.
Actually, now that I think back on it, the second method I used more than what I did in the picture - he didn't struggle nearly as much. Neither him or Muse did, actually. And I rested the syringe against my thumb and slowly fed the formula to him. It got it done a LOT faster.
You may find a different way works for you and him/her, but do not feed him on his back.
If milk starts coming out of its nose, you're feeding way too fast. One thing you need for sure is patience. One drop, wait......clean off his/her mouth in the meanwhile if you have to, another drop, wait..... It should be anywhere from 10 - 20 minutes to warm up the milk, give it to him, clean him off, and put him back to bed. It's very tiring, but very rewarding if you succeed.
Oh, it's also very important that you weigh him. One of the biggest signs that Farble wasn't going to make it is he started losing weight. I kept feeding him, doing what I was doing normally, but he kept losing weight, and then I went to feed him again 2 hours later, had already passed on.