There are a couple of ways to do this.

First determine where you want the outlet, then get a NEC approved junction box along with 12/2 Romex and some wire nuts.

Remember, since this outlet is in a bathroom, NEC Code requires that you use a GFCI outlet.

Next, kill the breaker that supplies the switch. What does the switch operate, an overhead light?

If it does, drop the light down and look for the wire connect of two black wires. This is the source line. It supplies power to the switch. Work the 12/2 wire from where you want the outlet to the source wire. Open the splice on the two black wires and pigtail the new black wire together with the other two wires.

The white wire needs to be pigtailed to the White from the source cable, not from the switch. THAT IS VERY IMPORTANT!!

At the other end, install the plastic box into the wall. I personally like my source wires to enter the outlet box from the bottom, so route the wire into the bottom of the outlet box from the bottom. Depending on the type box being used, secure the wire to the box per code. Strip the ends and connect the GFCI to the wires. Power on the breaker test the outlet by plugging in a radio or lamp. If the outlet is working, press the test button on the GFCI which should kill the outlet. If that works, turn the breaker back off and finish the assembly.

If you are at all unsure, get a qualified, licensed electrician to do this for you.

There is a fatal flaw in don-ump's advise: There is a reasonable possibility that the lighting circuit is a 15A circuit, and is likely to be shared with other rooms. Adding a receptacle to such a circuit in a bathroom would violate code.

The best way to add a receptacle would be to pull a new 20A GFCI protected circuit from your breaker panel. If you are not experienced with electrical work, I would suggest reading the book Wiring Simplified from cover to cover before going further. Or hire a pro.

Don-ump is also making another assumption that may not be true. He is assuming the light is part of a switch loop. That may not be true at all. The switch may be the power source, not the light. If there are only 2 wires in the lamp box, a black and white, and they are only attached to the lamp, then your power feed is at the switch.

I would strongly second the recommendation to read Wiring Simplified. It will give you much more detailed instructions than you can possibly get here.

Even better, they will be correct. ;-)

And I hate to say this, but it's truly necessary. Once again, Don has given erroneous information. This is getting to the point that it is becoming dangerous and the moderators should consider getting involved. I about died when I read his post and he didn't address the possibility the power is at the switch.

We know you're retired and bored Don. Perhaps it's time to take up gardening and post there. I don't want this to sound like a cheap shot, but seriously, your posts are getting dangerous.

To all,

Sorry if I am causing discontent across the net, I will stop answering any questions from this point forward. I may still ask questions if that is acceptable to you folks.

It never was my intention to disseminate bad info, so again I apologize.

FTR - I pulled my red book out and it is dated from 1976. Time for a new code book, I've ordered the 2008 book rather then the Red Book summary book;

Don

Don: I, personally, accept your apology, and think I speak for all of us by saying you're more than welcome to ask questions you may have.