You'll need to put together a minimum amount of equipment before you can begin sequencing. The most important piece of equipment is the sequencing program itself. The simplest sequencers are little more than recorders, gathering information produced by incoming MIDI signals for saving and playback. These are inexpensive to purchase, and easy to use, but you'll not be able to do much with the data once it has been recorded. Most sequencers at this level only allow for instrument replacement and basic editing of notes. On the upper end of sequencers, you'll have programs that give you the power of a full music studio, altering the MIDI signals in every way, and mixing MIDI with actual sound files to produce complete musical creations.
You'll need a quality synthesizer or wavetable soundcard to listen to what you're creating. Since you're dealing with data, not actual sound within the MIDI signals, what you hear is dependent, in large part, on the equipment you use to listen to it. The better your equipment's ability to reproduce the data as sound, the more accurate your work will be.
The final piece you'll need to make use of on your sequencer is the input device. Most sequencers will allow several different input devices. A mouse and keyboard are needed, at minimum. With them, you'll be able to input each note individually; this is much like composing by hand, except that with a sequencer, you'll be able to hear what you've scored immediately, and change it instantly. Another input method you can use is a digital keyboard. Digital keyboards offer the advantage of familiarity, along with allowing you to record precisely what you play. Most sequencers will accept input from any MIDI enabled device, so the choice on what to use is entirely up to you.
Editing your work is what the MIDI sequencer is really all about. Data is generally recorded to a single track. Once the data has been input, you can edit it using a variety of tools. The majority of sequencers present your recordings within an editable music score. The notes appear as they would on any piece of sheet music, and like using sheet music, you can alter the score in any way, moving notes, changing them in any way and assigning a different instrument to the track.
You can add tracks to the music while editing your piece. The process is the same with each track. Input the note, and then edit the track. As each track is added, you build the musical piece in complexity. You can assign a separate instrument to each track, using the same input device for each, while creating a complete orchestration. Tracks can even contain sound data in the form of wav files, though these aren't as easily manipulated as the direct data contained within the MIDI signals.
After you've built the piece you want, you can save it into a single MIDI file using the sequencer. This file can then be played with any MIDI compatible player or device, offering a note by note reproduction of your creation. With the aid of a few simple tools, you can use a sequencer to create any musical piece you desire.