How Do I Solder DC Motors With Flimsy Copper Pieces To Wires?

mirith:
the easiest way is to tin both the wire and the motor, then solder the two together so they are all in one continuous piece of solder.

I had a mind to comment earlier - it is not a bad idea to tin both the tab (both sides) and the wire, not leaving any more than a thin coating of solder - "wiping" the solder off with the iron is one of those skills. I always twist stranded wire before tinning, and pull back the insulation which will slip over again after tinning.

Then fold the wire over the tab - or insert it through the hole if there is one and (gently) crimp it over the tab, then you can quickly solder them together, adding a little.

For electrical work, you always use rosin core colder. As previously explained, finer solder gauges are preferable and provide plenty of flux.