Set your microphone to record your first vocal. Use a large diaphragm condenser mic, if you have access to one, for the richest vocal sound. Record as close to the microphone as you can without causing issues like noise artifacts from plosives (P-popping). Use of a pop filter is common for this application. Enable your DAW to record a track and set the level of your mic to record without distortion.
Set your headphones to monitor what you are singing. Keep the level of the headphones low so that the sound doesn't bleed back into the microphone; this may interfere with overdubs or, in extreme cases, allow feedback. Many singers prefer to have only one ear covered. If this is your preference, make sure the unused headphone cup is placed against your head or neck so no sound escapes.
Use both a metronome for tempo and a guide instrument for pitch if you desire. Record these to a spare track on your DAW. It is particularly important that these tracks do not bleed from headphones when recording vocals.
Record your first vocal. Replay the performance and re-record it, or sections you are unhappy with, a technique called "punching in." See your DAW manual to understand how your equipment and software accomplish this.
Disarm the recorded vocal track and enable recording for another track for the next vocal. Send the first vocal to the headphones as a reference. If it is possible, remove guide track and metronome from the headphones. Rehearse and record your second track. Repeat this process until you have all the vocals recorded.
Mix your acapella track on your DAW. This can be another very creative phase, as you can play with panning, equalization and effects to enhance your performances. When you are satisfied with the mixing process (which can take longer than recording), make a stereo master, using the method recommended by your DAW manufacturer.