I'll unfold the tire by hand, getting it as round as I can.
I then usually have to turn at least parts of the tire "right-side-out" because there are likely sections of the unfolded tire that are "reversed" with the body of the tire on the wrong side of the bead, outside-surface-in.
Once I get the tire as close to "round" and "right-side-out" as it seems like it's going to get, I start mounting the tire.
Note that it's never going to be as round as a non-folding tire. But it doesn't need to be that round to be mounted.
I'll start by holding one bead in the rim, then work around the rim, getting that one bead seated - note that the tire being "round" doesn't really matter now, other than being a bit easier to handle if it doesn't keep flopping in the way of working around the rim.
Once that one bead is seated inside the rim, I'll insert the tube, starting at the stem. I'll push the tire aside so the stem can be inserted (make sure you push the tire to the side that allows the tube to wind up on the inside of the tire - I may have done that wrong some time in the past...) and once the valve stem is fully inserted I'll work around the rim, inserting the tube into the tire as I go.
Once the tube is seated in the tire, I'll push the valve stem some to push the tube away from the rim to make sure that I can seat the second bead around the tube at the valve stem without pinching the tube between the bead and the rim.
After getting the second bead started, I'll work around the rim, seating the second bead. If the tire isn't too tight, I'll usually be able to roll the last section of the second bead over the rim with my hands. If that doesn't work, I'll use a Park Tool TL10 (a great tool - I have no idea why Park Tool discontinued it.) and seat the tire.