There are all kinds of them. From simple to sublime to ones the size of houses. I'll stick to the simple and the semi-sublime.
First, here's one your already own:
Once washed and the fingernails cleaned of axle grease, these work great. In fact, this is my personal pasta maker of choice. Clean-up is easy too. Just dust off your counter, wash your hands again, and you're done. Seriously, making pasta by hand is not only the fastest was, it gives the best result. The pasta turns out consistently smooth and silky. Here's a tip. Use 3 parts all purpose flour and one part cake flour. Your pasta will be the best you ever tasted.
At this point, you can either continue to make the pasta by hand or employ a cutter. To make it by hand, you need to first let the dough rest. Maybe an hour. Then roll it out thin. Then shape or cut it. I say 'shape' it because there are some pastas that you shape rather than cut. Like these cavatelli.
They're made with the flick of a finger or the tip of a fork. It is easy to do, but hard to describe. Farfalle (literally 'butterfly') is a shape that is both rolled flat and shaped. SparklyJr is our champion farfalle pincher.
My grandmothers (both of them) made pasta once a week and made a week's supply. They rolled out the dough on pretty much the same sort of homemade table shaped more or less like a wide ironing board. They both used a similar method, too. They rolled out great, huge, bed-sized sheets of pasta, so thin it was almost transparent. The rolling pin was one that is slightly tapered. They call these a french rolling pin.
The set up the table next to their beds. As they rolled it out, they allowed it to accordian fold onto the bed (protected by an old sheet for one and a special canvas sheet (so full of flour that it was probably waterprrof) by the other. Once all rolled out, they'd lay the sheet out flat on the bed and let it air dry for an hour or three. They then cut it into strips as wide as the wanted the finished product to be long. Roll up the strips into jelly rolls and then slice the noodles. Unroll each one (very tedious), toss them ina bit of flour, and store for a day in shallow layers on a table or the bed. They then stored the final, dried pasta in paper bags.
One gramma had a chiatarra like this:
Chiatarra means "guitar" and is pronounced 'kee TAH ra'. It is a series of piano wires strung across a board. The pasta dough, rolled flat, is laid on the wire. The rolling pin is then rolled over it, pressing the pasta through the wires and on the board. These are available in a narrow range of widths to make spaghetti and linguine or fettuccini.
You could also mix the pasta in a machine. A stand mixer or a food processor will work fine. I still prefer it handmade, though.
Then you need to cut it.
One of these hand crankers works fine. They also make motor accessories for some of these. There are a million brands, so if you want the motor, be sure you pick a brand that offers a motor accessory. They're not all interchangeable.
They make a similar device that fits on the end of your stand mixer.
Both Kitchenaid and all the various hand crankers have ravioli makers that use the same basic system. These metal units are easy to clean. Just dust them off and tap them. Let any leftover pasta just stay where it is. It will naturally fall out on the next use. Never wash with water as the metal parts are prone to rusting.
The last type of maker is the all-in-one mixer extruder. Like this one:
These work fine ... as far as they can go. Commercial pasta makers use machine cut bronze dies. These use molded plastic. The bronze dies get very hot from friction. This dries out the pasta as it passes through. The plastic dies don't. As a result the finihsed pasta could be a bit gummy. The broze dies are very sharp. The plastic aren't. Consequently the pasta shapes are a bit 'muddy'. The coomercial machines build up a lot of pressure. The small home machines don't. The result is a tendency for the pasts to sometimes 'shmoosh' its way through, leading to a sort of fuzzy appearance from a shredded surface on the shaped pasta. I wound up giving mine to one of my sons who is very happy with it (maybe cuz of the price?) These need to have all their parts disassembled, washed, and reassembled with each use. It is about the same level of clean-up effort as a food processor.
The last little device is this guy:
A BEEBO (brand) cavatelli maker. This makes just one shape - the cavatelli. They look like longer thinner gnocchi, but are all pasta dough, not potato/pasta dumplings. We love these cuz the cavatelli made on ths machine are perfectly chewey. Mixing my pasta by hand, I can go from thinking about cavatelli to eating cavatelli in about 15 minutes with almost no cleanup (assuming we have some gravy ready).
I you want a recipe for hand made pasta, lemme know.