Science involves your understanding of all the equipment - from the microphone to the recorder and then on to the final ‘mix down' - plus an understanding of studio acoustics.
Art is the ability to turn the raw ingredients into a musical masterpiece, this is largely at the mixing stage and lies outside the scope of this article.
Psychology is needed at the recording stage, if the singer feels good then they will give a much better performance. A song usually succeeds or fails on the strength of the lead vocal and it's this that the listener needs to empathize with.
Which Microphone?
There is no particular microphone you should use when recording lead vocals unless your vocalist has a very quiet voice, use a condenser microphone to avoid too much hiss being recorded. If the singer has a very sibilant sound you might like to experiment with a ribbon or dynamic microphone to reduce those high frequencies. Use a good windshield with a ribbon microphone to avoid damage when blasts of air hit the diaphragm.
A cardioid pattern is usually selected to avoid picking up unwanted sounds from behind the microphone, but it's worth experimenting with pickup patterns e.g. omni to see if you like more of the natural acoustic of the room.
If the microphone has a bass roll-off switch then you should be able to use 75hz to help reduce any mechanical knocks to the stand or foot tapping on the floor. The 150hz position risks making the sound bass-light. It's worth putting a carpet under the stand and the singer's position if there isn't one there already.
Different microphones suit different singers so experiment a bit while they get used to the track. Put out a handful of microphones if you have them and listen to each one to find out which is the best, then remove the ones you don't like, along with their stands, to avoid cluttering the studio.
Setting the Right Conditions
Some singers know what to do and when they've achieved it, others need lots of encouragement and directing. Sometimes you'll just have to accept that the singer's not on best form that day and arrange another session.
Offer to screen them away from the control room, the sight of people chatting or laughing on the other side of the control room window can be unnerving, especially for first time vocalists. Make sure that the singer has a comfortable balance between their voice and the backing track and a good overall level, offer them a bit of reverberation or effect on their voice. Use ‘closed-back' headphones to reduce ‘spill' of the backing track onto the microphone.
Some singers like to use just one side of the headphones to hear the track and listen to themselves clean with the other ear. Make sure that they keep the unused headphone completely in contact with their head to avoid spill.
If you're in a home studio ideally you'll have access to a separate room for the vocalist, if not you'll have to record in the same room as all the recording gear so you'll have to wear closed back headphones too and mute the speakers during takes. Be aware of machinery noise getting to the microphone, use a sound absorbing screen between the equipment and the microphone if you can.
Mixer or pre-amplifier settings
It's best to record vocals without too much processing i.e. equalization and compression, just concentrate on avoiding hiss (too low a level) or distortion (too high a level) since both are difficult, if not impossible, to remove afterwards.
You can use compression but only at low ratios, and/or a limiter set at a high threshold to stop the loudest moments from distorting. Don't record effects (unless it's on a separate track) or an electronic gate, leave these to the mixing stage. Like overly ‘wet' signals (lot's of reverberation or other effects), heavily compressed tracks can't be uncompressed.
Other useful hints
If you have enough spare tracks record all of the takes, including the warm-up ones, since some vocalists suffer from nerves when they think they're going for a take but are at ease when they think it's a rehearsal. Early takes are often the best ones before the singer's voice gets tired. Later you can compile the best bits from various takes onto one track.
If the singer isn't giving a suitably powerful performance it might be because they are hearing too much of themselves. Reduce the volume of their voice in the headphones and then they will sing louder and hopefully with more feeling.
Try to have as near a finished mix of the backing track for the singer to listen to, they will have a good idea of where they fit into the mix and you will be able to hear if the track is too busy in parts, rhythmically or frequency wise.