An adjustable front hub has a lock-nut on the outside, then sometimes a washer, then the cone which has two narrow flats. Cone spanners are thin spanners that fit onto the narrow flats. You need one that fits the narrow flats exactly. This is likely to be somewhere between 13mm and 16mm. Working on the wheel off the bike is easiest if you use an axle vice; a specially designed tool that fits in a bench vice. To use an axle vice remove any quick release skewer.
Front hubs are symetrical, they work either way round. It’s conventional to keep the right side locked tight and always adjust the left side. This is because if the left side becomes loose in operation, the turning wheel will loosen the bearing. If the right side comes loose, the turning wheel may tighten the bearing and cause catastrophic damage, or even a crash.
Unlock front hub
Screw the cone in or out to tighten or loosen the bearing on the front hub. When you move it out hold the axle still with a spanner on the cone on the opposite side. When you move it in hold the axle still with a spanner on the lock-nut on the other side. Make small adjustments and check the bearing between each.
Once the bearing is in the target zone of not-too-loose and not-too-tight hold the cone still and screw the lock-nut tight against it to lock the bearing on the front hub.
Check the front hub
Check the bearing and readjust if necessary. The act of locking may change the tightness of the bearing so if your first try at locking ends up too tight start again with the bearing very slightly looser.