I have a (admittedly rather cheap) pasta roller that I try to use fairly regularly. The issue is that when I am rolling it out,the dough keeps getting wider, not just longer, beyond the size of the rollers, and then getting all mangled at the edges. It also has a hard time feeding in straight. Every video I watch on pasta making doesn't seem to show this, so it is just some trick they aren't mentioning, the cheap machine, or what?
In addition to the answers already listed, the fact that you have a hard time feeding it straight might indicate that the rollers aren't quite parallel. Does it always go askew in the same direction? Does the mangled edge tend to be the same side?– AMtwoJun 22, 2020 at 14:06
You might be rolling the dough too thinly, too soon. Start by feeding a somewhat flattened 'disk' of dough through the pasta machine at its widest setting. Change the setting by at most 1 for each subsequent pass.
You might also benefit from 'laminating' the dough: after the first pass, fold the dough in thirds, turn it 90 degrees and pass it through the machine again. Here is a picture demonstrating the procedure from the Serious Eats "Science of the Best Fresh Pasta" guide.
(note -- I haven't rolled out pasta with a machine in 20 years or so, but I used to do it a few times a year with my mom)
I think this might be a sign that you need to let you pasta rest more, as it's not elongating easily.
If you don't have the time to do that, you can take a knife and cut the strip in half, with the assumption that they're going to get wider as you keep working it.
You can also fold it lengthwise for your last pass while you're working it on the widest setting before you start getting it down to the thickness you want.