Begin by experimenting with different ways to produce a note with your voice. Try to send the sound through your mouth, open and resonant. Then, try singing through the nose, like a Tibetan throat singer. You can achieve this by closing your throat off a bit to redirect the sound current upwards through your sinus cavity. Use plenty of air to make the note resonate.
Make a sustained vocal note resonate in all the other applicable areas of your body: mouth, sinus cavity, nose, chest, throat, torso and cheeks. Notice how much or how little air it takes to create resonance for each of these areas. Try low notes and high notes using a smooth glissando from the top of your register to the bottom and back up again. This will give you a good survey of how the different parts of your anatomy handle sound waves produced in the lungs and modified by the larynx.
Practice classical singing warm ups, such as scales and arpeggios, to make sure your singing chops are in order. Exercise your mouth with tongue twisters and the like. If you cannot sing without beatboxing, you certainly cannot do both at the same time.
Begin with the kick drum sound. This sound can be made with or without engaging the larynx to produce a note. For example, a bass drum sound can be made by grunting low and in your chest. (In essence, this sound is already a form of singing, as your larynx is being used to do so, and therefore "singing and beatboxing at the same time" becomes a redundant proposition.) On the other hand, a kick drum sound can also be made by buzzing the lips quickly and forcefully without using the vocal chords. Allow the sound to resonate in your mouth and sinus cavity. This sound is similar to that an electronic beatbox might make.
Try the snare hit, rim shot and hand clap. The snare sound is usually produced without the voice. Use your lips to buzz a snare hit (higher than that used for a kick drum sound). Alternatively, you can press the back of your tongue to your palate, build up air behind it and then release the tongue, sending it out of your mouth. This creates more of a rim shot or hand clap sound, both of which serve purposes similar to that of a snare hit in the context of a song, namely the offbeats.
Add tom-toms to your repertoire. This is a resonant sound. Use your voice to sing a note in your chest or throat, articulating with the tip and top of your tongue. Think of the word "dumm" or "bumm," but swallow the "uh" sound. Lead directly from the attack to the resonance, so that you end up humming for a very short time. This creates the tom-tom sound. Toms are very useful for human beatboxers. With an innate ability to modify the pitch of any sound you make, you can create an infinite variety of tom-tom tones to rival any drum set.
Add in the hi-hat, ride cymbals and crash cymbals. Metallic sounds like these are usually made by saying "tss," "tshh," "kshh," and so on. Of course, you should not use the voice for these types of sounds. Sustain the hits for as long or short as you like.
String together all of the sounds you are able to make. Put together a beat with kick drum, snare and a steady closed hi-hat. If you can get your own head bobbing to the rhythm, you can bet someone else will eventually enjoy your beatboxing, too.
Start simply. Try to produce one wordless note and one percussive sound at the same time. As discussed in Section 2, the combination of voice and vocal percussion is already inherent in some beatboxing sounds. Tom-toms, bass and kick drums, and snares are good examples of percussive sounds that translate easily to singing at the same time.
Get to know how sung vowels and consonants are similar to notes and sounds produced by beatboxing. Use vowels in sung words as moments for your beatboxing to resonate. Use vocal percussive attacks like "tuh" and "buh" as consonants in sung words. This technique allows your sounds to serve the dual purpose of creating part of a sung word and adding percussive content to your song. Efficiency--doing more with less--is the name of the game when beatboxing and singing at the same time.
String together a series of beats, notes, words, tones and melodies to create one line. You are now well on your way to being able to beatbox and sing at the same time. Practice seamlessly switching from percussive sounds in your throat to enunciating words in your mouth; incorporating "breaks" in which either your beatboxing or your singing shines on its own; and otherwise meshing each element of your overall repertoire.
Once you can convincingly mix up vocal percussion, wordless singing, singing with lyrics, and even imitating a few instruments (guitar and synthesizer imitations are good ones to try), try your hand at composing an entire song which you can rehearse. This is where creativity comes in. See how many ways you can surprise yourself. Experiment. Eventually, you will be able to improvise a great vocal beatbox with singing at the drop of a hat.