Midi Sequencer
If a composer wants to write music on the computer, writing music with a midi sequencer is the best way to do it.  A midi sequencer is a software program for Microsoft Windows or the Macintosh and enables a musician to edit music notes into the program.  The sequencer program holds the midi data, visually seen as musical notes.  The file of a midi sequencer is called a midi file.  Sometimes the midi sequencer will save the file as a sibelius, finale, cubase, or cakewalk extension.  In reality, these extensions are still midi files.  It is the job of a midi sequencer to allow the musician to edit musical notes into a staff or staves, and to save this data in a midi file.  The file can then be loaded again from the sequencer so the composer can edit the midi file.  There are different features that a sequencer can allow a composer to do, such as transpose music, damper pedaling, change the key signature within a measure, change the way the music looks visually, tempo change and much more. 
Midi Recording Process
1.  Midi Sequencer
2.  Software Sampler
3.  Gigastudio
4.  Sound Libraries
5.  CD Mastering

There are many midi sequencers on the market, but the best ones are Personal Composer, Sibelius and Finale.  These programs can help a composer write a musical composition into a notation form, and then save it as a midi file.  A midi sequencer is becoming common these days, as midi becomes more popular.  Every good composer in this day and age is using a sequencer, it would be stupid not to.  The traditional good old days of using pencil and paper are forever gone.  A sequencer is the best way to compose music, the neatest way, and most efficient way.  It is this step, writing music into a midi sequencer, and saving it as a midi file that is the first step to midi recording.

The second step involves the actual recording and converting from midi to mp3.  One way to do this is by using a microphone to record the midi file, into an mp3.  However, this method is poor, because not only will the mp3 still sound synthesized, but it won't sound as crisp anymore.  Another method, which is the correct way to record midi, is by using a hardware sampler, or software sampler.