Plumbing – How to connect plumbing to a trap adapter which is already installed

What size is that copper? You can get plastic p-trap kits in 1-1/2" and 1-1/4", and these can be easily connected to your copper via slip ring compression fittings. Basically they consist of a nut with a cone-shaped plastic washer, which when compressed by the nut squeezes against the (copper) pipe to create a seal. Usually these are only on the sink side of things and the wall side has glued-on plastic but you can use the compression fittings on both ends.

Here is a 1-1/2" Plastic p-trap

If you want to solder, a better solution than using a compression ring on the wall side would be to sweat on a copper x female adapter, followed by a male PVC adapter and a PVC trap adapter. Better yet if you can find one, just use a brass copper trap adapter like the following:

A less desirable but acceptable solution would be to use a fernco fitting to go from the copper to PVC, and then you can avoid soldering.

You'll need to install a drain assembly. In a bathroom, pop-up drain assemblies are common.

Here's an image of the drain assembly, with all the parts labeled.

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The tailpiece of the drain assembly, should attach to the trap assembly. If the trap is too low, an extension can be used.

When installing the drain, put a bead of plumber's putty around the drain hole of the sink. Then bed the drain flange in the plumber's putty. From below, install the washer and nut, and thread on the tailpiece. When you tighten it down, the excess plumber's putty will squeeze out. Use you finger, or a rag to remove whatever oozes out.