What happened to pumps? I'm an old-time bike rider who commuted to grad school every day for 3 years on a bicycle.  Then after a 20+-year-long hiatus, started riding again with my son.  I cannot figure out the fitting on the modern pumps.  I can get some air in, but after several cases of the thing flying off or making an embarrassing leaking, whoosh sound with every stroke.

Q: Are pumps with the  old-style, screw-on fittings available anywhere anymore?

Q: Is there a good reason I should appreciate the new fitting?
There are two main standards:  Schrader and Presta.  Schrader is the standard auto tire valve, while Presta is thinner and has a little knurled knob on top.  Schader is relatively straight-forward to use while Presta requires a little finesse.

Most newer "floor pump" valves are "agnostic" and will fit either style without conversion, but some require flipping a gasket over inside the chuck or some such.

Floor pumps generally have a flip-lever valve where you press the valve on, then flip the lever up to lock the valve on.  Sometimes, if the tire is flat, you may need to press your thumb into the tire on the back side of the valve to keep the valve from sliding into the rim as you push the chuck on -- if you don't then the chuck doesn't get on far enough.  Plus on some valves you may need to adjust the chuck by tightening a knurled fitting on the chuck, to compensate for gasket wear, etc.  And of course there are cheap pumps that won't work regardless.

Presta can be a little tricky.  You need to unscrew the knurled knob ALL THE WAY, then press the chuck on.  And I like to tap the unscrewed knob once to free the internal seal from its seat -- sometimes they stick, making it hard to get air in.  When you're finished filling a Presta, just tighten the knob barely finger tight, so as to not unnecessarily deform the seal.