Between a scene presenting itself and you pressing the shutter button, there are two calculations you or your camera need to make - the exposure settings and focus distance. Eliminating these calculations makes the shot happen faster, and makes the image more important than operating the contraption in your hands. Here is how.
1. Estimating exposure.
Many vintage cameras lack light meters. External light meters can be used, but that is one more gadget to carry around and slow you down. Both film and digital have a lot of latitude with respect to over or under-exposure, so you can worry less about settings and more about making a compelling image.
Just use the sunny-16 rule and relax. In summary, the rule means using f16 and shutter speed of 1/ISO in full sun. Drop one or two stops for cloudy conditions. This is an exact equivalent of shutter or aperture priority depending on how you reduce the light hitting your film.
This method is preferable to your camera's reflected light meter (if it has one) because you are essentially using an ambient reading, and you can ignore the apparent brightness of the subject (e.g a bright white building, or black cat).
With indoor light at night, I find I can shoot ISO 400 film at the equivalent of f2.0 at a 60th.
2. Zone focusing.
Just because we have auto focus, it is not necessarily the fastest way to focus. The lost art of zone focusing is to use a narrow aperture and set it to the hyper focal distance. This is much easier to do with vintage lenses with lots of distance scale markings. Lenses for modern digital cameras are not as easy to manipulate for zone focusing.
For example, I use f11 and set infinity to the '11' mark on my Rollei 35 lens for walking around cities. Anything 3 meters and further will be in acceptable focus - a picture is ready to be taken at any time.
TIP: 'Trim' your settings
Pilots use trim controls to keep an aircraft flying in a straight line without having to make constant corrections on the main controls. It compensates for changing wind and weight distribution conditions. In a similar way, I find I'm 'trimming' the settings on my camera as I walk around outdoors even when not actively shooting. For example, if clouds roll in-front of the sun, I'll decrease the shutter speed a stop or two. If I want the background out of focus, I'll set infinity beyond the hyper-focal range. Having the settings trimmed means not fumbling with the camera when a subject presents itself. Read more about the exact settings I use here.
Downtown Houston, Rollei 35s, Ilford HP5.