How do I do a garter eyelet border with mitered corners?

Does the number of stitches I pick up on each side of the blanket matter? And do I knit in the round or do I leave one corner open and knit back and forth? I feel like this should be so easy to figure out and I am having a total mental block - argh!!!

Yes, the number of stitches picked up matters. If you pick up too few, the edging will pucker and fold in onto the blanket; too many the the edging will ruffle. Picking up 2sts for every 3 rows garter or 3sts for every 4 rows stockinette is a good place to start but you may have to experiment to get it right for your blanket. At the corners you should pick up more sts, maybe 2 in one row a couple of times to make sure that you create extra border to turn the corner without folding over too tightly.
You can do this in the round or knit back and forth and then seam the open border. If you knit back and forth, put the seam on a long edge, not right on a corner.
The video on picking up sts may help too.