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To get started, you should master the three basic sounds of beatboxing: the classic kick drum {b}, the hi-hat {t}, and the classic snare drum {p} or {pf}. Practice combining the sounds into an 8-beat rhythm like this: { b t pf t / b t pf t } or { b t pf t / b b pf t }. Make sure to get the timing right. Start off slowly and build up speed later. The simplest way to make the classic kick drum is to say the letter "b." To make it sound louder and punchier, you need to do what is called a lip oscillation. This is where you let air vibrate through your lips - a bit like "blowing a raspberry." Once you can do this, you make a very short lip oscillation.  Make the b sound as if you are saying b from the word bogus. This time, with your lips closed, let the pressure build up. You need to control the release of you lips just enough to let them vibrate for a short amount of time. Make a simple "ts" sound but have your teeth closed or lightly closed. Move the tip of your tongue forward behind your front teeth for a thin hat sound and to the traditional t position for a heavy hat sound. Breathe out for longer to create the open hat sound. You can also do successive hi-hats by making a "tktktktk" sound, using the mid-back of your tongue to make the "k" sound. You can make an open hi-hat sound by drawing out the breath in the "ts" hi-hat, so it's more like "tssss" for a more realistic open door sound. Another way of producing a realistic high-hat sound is to make a "ts" sound with your teeth clenched. The simplest way of making a classic snare sound is to say the letter 'p.' However, making a 'p' sound is too quiet. To make it louder you can do several things: the first is to make a lip oscillation. This is where you push the air out of your lips making them vibrate. The second is where you breathe out at the same time making a [ ph ] sound.  To make the 'p' sound more interesting and more snare-like, most beatboxers add a second fricative (continuous) sound to the initial 'p' sound: pf ps psh bk. The variation {pf} is similar to the bass drum, only you use the very front of your lips instead of the side, and you tighten them more. Pull your lips in a bit so that your lips are sort of hidden, as if you had no teeth. Build up a little air pressure behind the hidden lips. Swing your lips out (not literally swing) and just before they return to their normal position (un-hidden), release the air with a 'p' sound. Immediately after you release the air and get the 'p' sound out, tighten your bottom lip up against your bottom teeth to make a "fff" sound.
Understand that there are many sounds to master. Practice the classic kick drum {b}. Next, try to duplicate the hi-hat {t}. Try successive or advanced hi-hats. Try to tackle the classic snare drum {p}.