OK - so first I'm going to tell you a few things that I assume are already done - if they aren't or they are done differently the direction I give may not work.
a - You have the outside of the bag finished (side seams and bottom seam).
b - You have basted/sewn the little tabs that hold the handle (with the handles in them) to the top of the bag. The raw edge of the tabs should be even with the top of the bag making the handles hang upside down for now.
c - You have the bag lining finished (side seams, bottom seam, and pockets sewn on if there are any) and you have left a hole in the middle of the bottom seam. It is easier to close up the bottom if you don't leave the whole seam open but with those handles and to do the understitching you need to leave a fairly large hole, I'd sew 1" or so, backstitch for security, skip over to the last 1" or so and sew again backstitching for security.
If these things are true what you do next is:
1 - Turn the bag itself inside-out. Have the handles and tab thingies down inside as well.
2 - Turn the lining right-side-out and place it inside the bag.
3 - Pin around the top of the bag, matching the side seams.
4 - Sew around the top of the bag. I always sew twice - or at least back stitch over the handles (tabs in this case).
5 - Pull the lining out. The whole thing should be inside out and looking kind of weird - like a bag on each side.
6 - Understitching - the purpose is to stitch the seam allowance to the lining so the lining will lay inside the bag nicer. It is going to be a little difficult since you are working through that 8" whole in the bottom of the bag. The Secret Pocket
has an online tute with pictures that explains it better than I can in this small space. Note that she talks about "facing", "collar", and "lining" in the tute and they are all interchangable for the purpose of explaining understitching.
If the understitching is too difficult through that hole in the bottom seam you could simply turn the bag right-side-out, tuck the lining inside the bag, press the top edge very well, then neatly topstitch or edgestitch (basically topstitching close to the edge) around the top of the bag which would sew the bag and the lining together thus keeping the lining inside the bag.
PS - I'm glad I searched understitching for you because that Secret Pocket blog has some very useful technique tutorials that I had not seen before.