Cut the seams. See the map.

A UV map tells a flat image where to go on a 3D model. Read it, mark seams and unwrap a cube and a cylinder, see why a closed object cannot unwrap without cuts, use Project from View, Cylinder and Sphere Projection, and tidy up with Smart UV Project, Pack Islands and Average Islands Scale. A copy of Blender's UV Editing workspace, with the same keys.

STAGE
    LayoutModelingSculptingUV EditingTexture PaintShading
    Color Grid
    LMB select · Shift add · G S R · Wheel zoom · MMB pan · Home
    LAB VIEW
    MMB orbit · Shift MMB pan · Wheel zoom · Numpad 1 3 7
    KEY IDEAS

    From 3D to flat

    A UV map is a flat copy of the surface. Seams say where it may split; unwrapping and projections decide the shape of each piece on the image.

    U, V
    The two coordinates of the image: U across, V up, both from 0 to 1. Every corner of every face has its own pair.
    UV island
    A group of faces that stay joined on the image. A seam edge appears twice, once on each island border.
    Seam
    An edge where the surface may split when you unwrap. Red in the 3D Viewport. It does not change the model.
    Unwrap
    Flattens the selected faces with as little stretch as possible, cut at the seams. A closed island cannot be solved.
    Projection
    Sends the image onto the faces from a direction: the view, a box, a cylinder or a sphere. No seams needed, some stretch.
    Stretch
    How much the image is squashed on a face. Display Stretch colours it: blue none, red a lot.
    Pack · Average
    Pack Islands places the islands in the square without overlaps. Average Islands Scale gives them the same pixels per metre.
    0–1 square
    The image. UVs outside it repeat the texture (tiling); for painted or baked textures keep everything inside.