My Pentax A3000 doesn't have shutter speed control, only ISO and a few modes, B (bulb), 60 for flash, program, and aperture. I keep it on program, but what should I do if I want to shoot in darker lighting? Since I'm using 400 speed film, do I have to keep the ISO on 400?
In short: it's kind of a pain, because this camera was targeted at people who didn't want to worry about such things. It only has fully-programmed and aperture priority mode. As you've discovered, there's no way to set shutter speed directly (other than bulb or flash sync).
The camera's exposure program uses the built-in meter and automatically matches aperture and shutter values to give its best guess at correct exposure for the scene. (It's not smart — it just assumes what you're pointing at should be average gray.)
It has an "exposure compensation" button, but that is fixed at changing by +1.5 EV — it's meant for the common situation of a shaded subject with a bright background. More sophisticated cameras often have a range of exposure compensation settings.
So, you can, to some degree, fake this by playing with the ISO setting. That setting tells the camera the sensitivity of the film you have loaded — of course, unlike with a digital camera, you can't adjust that from frame to frame, but what you can do is trick the camera into giving a brighter exposure by setting the ISO value to be lower than it really is. Then the camera's program will pick a longer shutter speed to get in more light. (Or possibly also wider aperture, if you're in full program rather than aperture-priority mode.)
But, really, I think if you're interested in more control, I suggest you look for a different camera body. The Pentax K1000 is an all-manual model which is still highly regarded. It's kind of the opposite of this camera, in that there's nothing automatic. (But it does have an easy-to-use exposure needle.)
An aside: if your A3000 came with the 50mm f/1.7 lens, keep that — many other low-cost Pentax cameras have the f/2 instead, and the f/1.7 is far superior in every way (not just the faster aperture).