It don't got a hole to stick the wire in to solder the connection.
View attachment 147325
We used to call this "Tack" or "Contact" soldering.
Essentially, You want to place the wire between your soldering iron tip and the center post connector. Then apply solder to the *wire* and let it flow over the wire and the connector. Make sure you have a solder sucker handy if you mess up, and do not over heat the part trying to get it. Also, make sure you do not move the wire at all unless the solder has fully set or you may create a cold solder joint which may raise the impedance of the circuit, or sometimes leave the circuit open.
It looks like that socket is designed to ground to the body of the
mod... so attaching a ground wire may be unneeded.
If you are working in a non-conductive material, you'll need to solder a ground wire to the inside lip of the 510 connector. Use the same process I outlined above.
If you've never done this before, expect to become frustrated.