I agree with jan: Pull the yarn through to the inside and secure it there- But I do not go through the dead center but through a stitch on the side, through the middle of a stitch, actually. That makes it even a bit safer, I think.
Oh, I have seen people do it either way but for me there is only one way to pull the yarn through:
when working in the round or when closing up stitches that will be like on the top of a hat / mitten, lying in the round:
I do take my yarn end from the stitch that I worked last of all to the stitch that was the FIRST of that round. Hard to write down... I go against the direction of my stitches, so the yarn gets pulled through the stitches in the order of the last round they were knit in, ending with the stitch I knit last.
In my eyes that closes the round better. Which way have you been going around?