Insulate a copper wire in home condition
The way to have insulated copper wires for magnets is to buy magnet wire. This is insulated with a thin but tough layer of varnish-like insulation. Often it's copper-coloured, and it's easy to think the wire is bare, unless you've met it before. 

There is no practical way to try to replicate this with bare wire and household materials like insulation tape (too bulky) or paint or varnish (you'll never get a well-adhered tough even film). 

If you don't need much, then unwinding an old transformer (motors less so) can provide a useful source. However, the kinks in the wire from first use can make it impossible to wind neatly, and the insulation film, though tough for a film, is still fragile enough to be damaged by rough handling, so this second-hand wire source is definitely second best.