I am new to woodworking and I am trying to reproduce a picture frame I found in a catalog. I wonder how they achieve a slightly rounded edge (see picture below).
I suspect that they use a router and router table, but I can't figure out what bit they would use. Can someone please help me understand how this can be done?
A router is overkill for doing a very slight roundover like this, although it will do the job well and very repeatably of course once you've dialled in the setting on the router or the router table.
As already described well in the Answer from @rob, you can do this sort of thing very well with a hand plane*, followed by light sanding with finer paper (whatever your finishing grit is). But not everyone has a hand plane or wants to get one so it's important to mention that you can do this simply by sanding alone.
This is one of the few times I'd recommend sanding as a viable shaping technique, but here it's appropriate since it's such an easy thing to do and it gives such good results. On an edge like this perhaps two passes with 80 or 100 grit paper (using a soft block or with the paper backed just by your fingers) followed by a couple of passes with 150 or 180 paper will give you very even, consistent results just about any time you need it.
No setup involved, just a few moments' work and after a quick dust off you're ready to apply finish.
*Doesn't have to be a block plane, they're just handy because they can be used one-handed with the work held by the other hand. Mind your knuckles doing this on narrow stock!
You can use a roundover bit in a router
You can use a router table or not, and there are several different size roundover bits. In your picture, it looks like maybe a 1/8" bit was used.
You can also round over the edges slightly while sanding. This may be the better option if your picture frame isn't very big and/or you're not looking for a big roundover. You'll be sanding anyway, so rounding the edges is an easy thing to do at the same time, and doesn't require getting out the router.
Product links / images are for example only
You can break the corners a few times with a block plane set to take a very shallow cut. First make a 45 degree pass to make one facet, then break both corners of that facet, repeat on both corners of each additional facet, and so on, as needed until it is sufficiently rounded. With each pass, it will get closer to being round. You can sand lightly to further smooth it out.
