I presume your Alesis synth has MIDI capability.
Let's say that you record to hard disk on PC, and you have USB on the PC, you're running Windows 2000 or XP.
You load a sequencer on the PC, say Noteworthy Composer from
www.noteworthysoftware.com (cheap and great to use).
You write some notes in the package, and you intend to drive the synth from the sequencer.
If you're on a desktop PC, you can connect a midi cable from the sound card MIDI output to the midi input on the synth. You set the midi output device on the Windows control panel to the PC sound card.
If you're on a laptop you'll need a device like an Edirol USB midi cable (UM-1)
www.edirol.com if your laptop PC has no soundcard ins or outs.
When you play your sequence on the sequencer, the notes sound on the synth.
Now, if you run an audio cable from the synth line output to the sound card line input on the PC, you can then record your synth on a recording package such as n-tracks (
www.fasoft.com) or similar.
Again, if you have a laptop, you'll need a second USB port, and a device like a Tascam US-122
http://www.tascam.com/product_info.php?pid=253
or an Edirol USB conversion box like a UA-20 or UA-1 or similar (
http://www.edirol.com/products/audio.html).
Both the sequencer and the recorder can operate on the PC at the same time.
Another option is to save/export the midi sequence from the sequencer as a midi file, and import this direct to recording package like n-tracks, as a midi track, then drive a soft-synth from this track inside n-tracks.
So there's a cheap way to set yourself up - about $110 for the registered software, and about $230 in midi and audio interfaces if your PC is a laptop with two USB ports.
There may be other options, but I'm simply recommending something that I have in use here which is cheap and quite effective.