The caulk should stick if the underlying surface is clean. I'm not sure if there's a difference in what the caulks stick to, but you should look into it. There are two major kinds of caulk and a blend: acrylic, silicone, and acrylic/silicone mix. The acrylic dries hard, the silicone stays squishy, and I haven't used acrylic/silicone, but I'd imagine it's less squishy when dry.
For smoothing, a finger works great, but don't use your bare hands! Wear disposable latex gloves the entire time you're caulking. You don't want to get the caulk on your hands. This also makes it so none of the caulk sticks to your finger as you smooth the caulk bead.
I recommend against using painter's tape, because when you remove it, you end up with weird vertical edges to your caulk that make a great grip for ripping your caulk right back off again. The bump is kind of unsightly, too.
Instead, be sparing in your use of caulk. If the gap is large, don't use a huge caulk bead. Instead, get a backing rod, slip it in, and then caulk the gaps between the backing rod and the surface.
I also recommend a colored rather than clear caulk. (Probably only silicone can be clear, but still.) You probably don't want to see the crack through the caulk, and the clear stuff seems to look dirtier as it ages. (I have vague memories of it actually yellowing over a couple years.)