Here's the way I like to make vines.
First I starch the fabric heavily. This makes it easier to cut accurately and go through the bias tape maker tool easier. I use a 50:50 solution of liquid Sta-Flo starch and water, "painted" on to the fabric with a large painter's paintbrush. My kitchen island is perfect for this. I throw the fabric in the dryer, then press with steam. This makes the fabric quite stiff.
There are different ways to cut the strips. The easiest way for me to find the bias line is to turn up a corner of the fabric until it is aligned with the selvedge, and iron in that crease. Basically you turn the fabric so you have a right triangle; the long side of the triangle is your bias line.
After cutting along the crease, I use my rotary cutter and ruler to cut parallel strips of the correct width. (Width depends on how thick you want your finished vine to be.) I piece these strips together, placing the seams at a right angle similar to the way you would piece a binding. Trim off any excess fabric at the seams.
I really like the Clover bias tape tools at this point. Basically you just start the fabric through the little tool, ironing it as it comes out. Once I have the iron on the end, I just pull the tool by its handle a way and iron as I go. This tool folds the fabric on both sides, so you end up with a bias strip that has the ends folded under. The strip itself, because it is bias, can be made to conform to curves. The thinner the strip, the tighter the curves can be.
There are other ways to make vines, but I find that this is the fastest and easiest for me. The Clover brand bias tape makers come with different colors of plastic to help make size identification faster. Each width contains directions about how wide to cut your strips to feed through.
HTH!