There are many explanations on the intertubez that 'explain' how to graft garter stitch. Badly and/or incorrectly, as I found, to my sorrow. I turned to Ravelry where ZaftigWendy explained it very clearly. I was gonna try to explain it myself, but then I realized I could show you what she told me:
The hard part is that for grafting garter stitch, you have to pay attention to whether you have knits or purls facing you.
If you hold the two needles to be grafted in your left hand with the knitting hanging down, just like you would when grafting a sock toe, then you want the last row of EACH of the two needles to have purls facing you. When you graft a sock toe, the front needle has knits facing you and the back needle has purls facing you. For grafting garter, you want them BOTH to have purls facing you. If you don’t, then knit one more row on ONE of the needles, and then arrange them again.
Once you have that, it’s easy. Start with going purlwise through the first stitch in front and pulling the yarn through. Then do the EXACT SAME THING on the back needle.
Then go knitwise through the first stitch on the front needle and remove the stitch from the needle, then purlwise through the next stitch. Then do the EXACT SAME THING on the back needle.
Repeat until all the stitches are gone.
She also found a video
Hope this all makes sense!