Unwrap a cylinder

A cylinder comes apart as three pieces: its two round caps, and its side, opened along one line to lie as a rectangle.

In one click

1. Open File and, under Examples, with Pre-unwrapped unticked, click the cylinder under Primitives.
2. Click Generate UVs. The caps come off at their sharp rims and lie round, and the side opens along a line to lie flat.

By hand

1. Open the bare cylinder again, and press 2 for Edges mode.
2. In the 3D View, double-click an edge of the top rim to select the whole rim. Then Shift+double-click an edge of the bottom rim to add it.
3. Shift+click one of the upright edges down the side, from rim to rim.
4. Click Split, then Flatten.

The upright seam is where the texture's two ends meet round the side: put it where it's least seen, such as at the back.

Check it

Pick Stretch in the Textures section's Preview, as Generate UVs does by itself: the caps and the side come out blue, true to their shape. Pick Color to see its squares run straight round the side. See Stretch and Texel Density.