The answer is dependent on the hub, and whether you have a cassette or freewheel hub. If you don't know the difference see
this. I presume you meant axle when you said skewer.
Generally speaking for a freewheel hub it is easier to access the drive side race with the freewheel off. For cassette hubs the drive side race and bearings are generally only just inside the freehub so it is not so necessary to remove the cassette before servicing the axle and cup and cone bearings, see
this.
To remove the freewheel you need a freewheel remover which is dependent on which kind of freewheel you have per
this. For cassette removal you need the correct lockring remover and a chain whip. The only tools you need to overhaul most cup and cone bearing hubs are correct sized cone spanners. Spanner size requirement depends on make and model of hub.