The linked tutorial seems to be highly optimistic that tacking the folded-over raw edges with a couple of whip stitches here and there will do the job. I use my bags until they fall apart (unless they’re special-occasion-only bags), so I need to start with more sturdy attachment methods.
I suggest following the tutorial’s method for forming the bottom of the bag (fusible interfacing + satin fabric). I would also sew, with a sewing machine if possible, a straight line of stitching approx. 1/4 inch (5 mm) away from the finished edges of the bottom, all the way around. 10 or so stitches to the inch is fine; 12 is OK; 15 is likely to damage the satin. This is your insurance for when the fusible’s adhesive begins to fail in a year or two (my experience).
Then, when the edges are folded over on the fabric for the sides of the bag (I can’t quite tell whether her instructions also provide for the ends of the bag), I would either hand-sew those edges completely down or, again, machine-stitch them in place.
Next, attach the bottom of the lining to the sides/ends of the lining. Here I very [B]strongly [/B]recommend hand stitching, because you’ll want the flexibility that hand stitching can provide. Don’t absolutely nail these pieces together within an inch of their lives; you [B]want [/B]them to bend up from the bottom towards the top of the bag. 
Now we can finally address your original question: how to attach the lining to the knitted bag?
At this point, you have 1) a finished edge (the sewn, turned-over fabric) at the top of the lining and 2) your knit fabric.
Depending on whether or not you like the appearance of your hand stitching, and whether you’d like to make the stitching a feature or conceal it, make your thread selection (i.e., either contrast or matching). Sew from the inside, but make sure you can see both fabrics at all times. Catch the yarn of a knit stitch and, in the same pass of the needle, catch a few threads of the lining. Pull the needle through. Advance to the next knit stitch. Repeat. You’ll be overcasting the two pieces together, all the way around the bag.
I try not to split the yarn with the needle but rather to encompass the entire strand in each stitch; splitting the yarn can lead to weakness in the seam.
I’m sure the bag will look terrific!
