I'm trying to insert an His-tag in my plasmid using fusion PCR, but I'm not sure how it actually works. Is the primer like having a long tail of our fragment that we want to overlap with our sample?
WIth gene fusion by overlap extension you have to design complementary primers with half of each primer corresponding to the first/last part of the genes you are fusing. These primers are normally about 40bp long. So in your case you would have the first part of you complementary primers corresponding to the last 20 base pairs of your plasmid and the next half of the primers coding for the first part of your histidine tag. Then the same for the other end of the tag and plasmid. So in all two sets of two complementary primers. The primers will anneal half of their length to the plasmid and the other half will anneal to the tag which is why the primers are about 40 bp instead of the more common/recommended 18-240ish length of common primers.
Fusion PCR is great to fuse things together by PCR. Here, you want to insert something in a plasmid. I do not see any reason to use fusion PCR for this. You could fuse the plasmid to the insert by fusion PCR, but then you end up with a linear fragment, so that is not helpful. Best is to do this by regular cloning, or Gibson cloning. Gibson cloning is "fusion" like, but it is not fusion PCR. The ref for Gibson cloning is: Enzymatic assembly of DNA molecules up to several hundred kilobases.
Gibson DG, Young L, Chuang RY, Venter JC, Hutchison CA 3rd, Smith HO.
His tag is pretty short, 6 AA, 18 bp, you can add that directly to 5' end of your primer like you would normally do with a restriction site. It might even be possible to get a restriction enzyme recognition site within or overlapping with that extension. So the total length of the mutagenic primer would be around 40-45 bp.
Perhaps the answer is to cleave the plasmid at the required his tag insert site and design just two complemetntary primers which will rejoin the plasmid with your his tag in the middle of the cleavage site, this should work if the tag does not need to be too long.