Purchase a MIDI controller and beat-making software. M-Audio makes a simple MIDI controller that is small, portable and affordable. FL Studios is the easiest beat-making program to learn.
Decide what type of tempo or meter you want your instrumental to have. The most typical meter for rap music is the 4/4 with a tempo of about 95 BPM (beats per minute). This varies depending on the style of rap you want to make. The Southern style of rap known as "Dirty South" usually has tempos at either 110 to 120 BPM or 75 to 90 BPM. East Coast-style rap is typically 85-95 BPM. West Coast-style or "gangsta" rap is between 95-100 BPM.
Make a bass drum pattern for your song. There are a number of different types of patterns you can make. One typical for West Coast-style rap is to have the bass kick on the first and third beats of a measure.
Add a snare drum to your bass drum pattern. The snare usually hits in between the bass kicks and can be arranged a number of different ways. To continue the West Coast rap example in the previous step, the snare would go on the second and fourth beats of the measure.
Throw in some high-hat cymbal percussion. A good solid hat pattern would be to have the hat hit on the first and third beat of the measure. You can also have the hats hitting on all four beats in the measure.
Add instruments to your beat. You can add guitars, bass, piano and synthesizer melody arrangements to really bring out the emotion of your instrumental.
Arrange your beat into verse and chorus sections. For this, you will simply just add and take away different melodies. You also can change up the drums for the chorus if you prefer. Save the finished beat as an MP3.