What's the best way to hang frames and shelves on plaster walls?
I live in an old house too.   I'll assume yours, like mine, has some history to it and has been renovated and altered over the decades.  You can't do DIY in an old house the way you can in a new one.  You can't follow simple repeatable rules. You have to learn how different walls are built and how different fittings behave.  Your handyman's secret is experience and adaptability, and you need to develop that yourself.
In my house, some walls are plaster over lath, some are plaster over backing board, drywall over plaster, two layers of drywall over plaster, two layers of drywall directly on studs .... you get the picture?   Yours may not have as much variation as mine but you'll have to learn what different materials feel like, learn what works in different kinds of walls, and you'll have to make mistakes and learn from them.
Let's assume most of your walls are plaster over wood lath.  I've found that usually by drilling appropriately I can hang most heavy things (not shelves) on that.   My &quot;secret&quot; ... Use longer screws than you would for drywall.  Drill a small hole and feel your way.  You can usually tell when you transition from plaster to lath.  Keep drilling to see if you've got a stud.  If yes, just use a 2.5&quot; screw and you're good to go with anything.  If you don't hit a stud then drill a larger hole into the plaster but not through the lath, large enough for a plastic anchor.   Insert the anchor, which will stop at the lath, and cut off the excess.   Then use a 2&quot; screw.   These are pretty strong and a couple of them will hold up almost any picture.
For shelving you have to find a stud.   Sometimes a magnetic stud finder will find the lath nails but not usually.  Sometimes it's just trial and error.  Either drill lots of tiny pilot holes til you find a stud or drill a 1/2&quot; hole and insert an endoscope to find it.
There is another solution:  Don't hang shelves on your plaster walls.  Buy standing shelves.  Pretty much anything else can be hung safely by developing an understanding of how different screws and anchors behave in different materials.
One last bit of advice: Join the Facebook group &quot;Historic Home Renovations&quot; and share your questions and experience there.
Good luck!
EDIT: I should have added the possibility of a really good stud finder.  There are new ones, quite expensive, that pair with a phone app to show you much more than a traditional stud finder can.   I don't have one and haven't spoken to anyone who has used one successfully in an old house.  Everything I know about them is from their fancy youtube infomercials, and of course according to those they can find a postage stamp hidden behind a concrete block wall.  Or something like that.  Maybe worth a try ... and you still need to get to know your walls to use one of those successfully, in other words they are not magic, but they might help a little.