First off, are you going to use a tripod when taking your indoor shots, and will there be any moving objects in your photos? A slow shutter speed can cause blur due to camera shake and faster moving objects can appear blurred too as they've moved while the shutter is still open.
Secondly, what do you mean by neon lights? True neon lights are those old fashioned, coloured thin tube type ones like this:
https://en.wikipedia.org/wiki/Neon_lighting Once we know this it should be easier to help you (hopefully!).
I have a Canon A1 too, and it's got quite a reliable built-in light meter, with a numerical read-out display at the bottom of the viewfinder, which shows the shutter speed and aperture settings. The meter is fairly 'centre weighted', meaning that it tends to concentrate more on what is in the centre of the frame when you are aiming the camera at something. If the room is fairly evenly lit it should cope pretty well. However, if there are bright and dark areas you will probably struggle to get everything looking even and you may well have to decide if you want to expose for either the light or the dark areas, as you may not be able to get both 'right' in the same photo. If you understand the basics, you could try
exposure bracketing in '1 stop' increments and see which photo you like best?
https://en.wikipedia.org/wiki/Bracketing
Anyway, putting things like that aside for a moment, the A1 came with quite a comprehensive instruction manual which covers how to use different exposure settings, and is available here if you haven't got a copy:
http://www.cameramanuals.org/canon_pdf/canon_a1.pdf I re-read my copy every so often just to refresh my memory on which setting does what; it's a pretty advanced camera if you want it to be, or quite tame and easy to use if it's set to full auto, and I love it for that.
Perhaps the best thing to do would be to read the manual through thoroughly, try taking a test film, make some notes on what settings you've used when taking each photo and come back to us with the results if you feel you need any suggestions or help. There are plenty of experienced film photographers on here and I'm sure they'd be pleased to help you. Most of all, don't give up, it takes a few rolls of film and a few failures to get the hang of things...
in fact I think a few of us are still trying get the hang of things 20 or 30 years on!
Hope this is useful, best of luck and have fun.