WindowGrid is a lightweight free tool which allows users to move and resize their windows to a customisable grid, using just the mouse.

To use it, left-click the title bar of a window as usual, and begin to drag.

If you decide you need WindowGrid, hold down the right mouse button as well as the left. (If you continue dragging with just the left button down, as normal, everything works as usual.)

A grid overlay appears (you can customise the size in WindowGrid's settings). Your window snaps to the nearest grid line and resizes to fit.

Continue dragging the window until the top left corner is snapped to your preferred grid position.

Release the right mouse button only, and drag down and right. Your window resizes, snapping to the nearest grid position.

Release the left mouse button and that's it: your window has been snapped and sized to fit a specific position on the grid. Relocate other applications to fit around it, and use them as normal.