Just to get the ball rolling and to welcome you, yes, it is easily done.

All you need is your turntable set-up and a connection to one piece of gear between it and your computer - or maybe even a card for your computer and the table directly in!

I am a Neanderthal at the specifics, but someone will be along shortly to better explain what to buy and how to do it!

Also, a piggy-back question to whoever that is: would that modded up Alesis Masterlink recorder be able to do that?

Anyway, welcome again.

Phono Preamps

First you will need a phono preamp to raise the millivolt level of your TT/cartridge to a couple of hundred millivolts to be able to record into your sound card.

Look at the TC 750 which has a volume control to help you keep your levels up, but not into "over-land". Overs in digital are very bad. You will have to watch your recording software's input metering to keep you below 0db. This unit is not the highest audiophile quality (look at the price), but does offer a volume pot to control output levels.

Most recording software has "normalizing" to bring the levels up to zero for you. This way all your tracks will be of equal output level will preclude you from keeping tabs of the playback levels.

Your problem will be time, as all this must be done in real time. Their is no truncating back from 78 rpm to 33.3. LOL

Better quality would be a good phono stage from someone like Needle Doctor.
You would then need a output level control like a Creek OBH to keep the levels in line. The line out of the phono stage would go into the input of the Creek and the output into your computer. It is not as complicated as it sounds.

The other option is to find a used system preamp with a phono stage built as on the Stereophile AV marketplace. I have seen some NAD, and Adcom units under $200. You could then take the preamp variable output into your computer sound card and do the same thing.

The TC 750 is the cheapest and the easiest. You will just have to decide if the sound quality is good enough. Regards.