Grab a ship with a claw

Close a Grappling Claw on another ship of yours in orbit, one with no docking port, so the two fly as one — then pump its tanks and let it go.

Use this to catch a spent stage or a derelict, to add a ship to a station whose ports are all taken, or to drain a tanker that was never given a port.

The ship you are flying carries a Grappling Claw facing out where it can reach the other ship, and its Armed switch is on (it is, unless you turned it off).
The ship you are flying carries RCS Thruster Blocks and hypergolic propellant to feed them.
Both ships are in orbit around the same world. If you want the other ship's propellant, the claw sits straight on one of your tanks. Why is on Rendezvous and docking.

Steps

Fly to within a few metres. Find the ship, close the range and kill the relative speed exactly as for a docking: steps 1 to 6 of Dock two ships.
Pick the part to grab. The jaws close on the side of whichever part they reach. For its propellant, aim at a fuel tank, not at the pod or probe core on top of it: fuel only crosses into a part that carries fuel.
Line the claw up. Use the two turn keys until the claw points straight at that side of the part, inside 35 °. Both ships must be steady, not turning against each other.
Drift in on the sliding keys. Use short presses and keep the target chip reading CLOSING at well under 1 m/s. The jaws close on their own once they are within 1 m of the hull.
Move what you came for. Tap one of your tanks, tap Transfer resources, and pick the caught ship's store on the list. See Transfer resources between stores.
Let go. Tap the claw and tap Release. The two ships are pushed gently apart and the one you caught flies on by itself.

What you should see

When the jaws bite, the toast reads "Grabbed" and the other ship's name and the banner reads GRAPPLED. The ship you caught is turned square onto the claw and is part of yours now: it is gone from the map as a ship of its own, and its stores are on the transfer list under its own name.

A probe-flown tug with its claw closed on the side of a crosswise fuel tank on a second ship, the toast reading Grabbed Derelict. — Grabbed by the tank's flank: the other ship had no port at all.

If nothing grabs, you were too fast, too far off square to that side, too far out, one of you was still turning, the claw is disarmed, or the ship is another player's (a claw holds only your own ships). Back off, steady both ships and come in again. Release stays greyed on the claw's sheet while its jaws are empty.