Using a vintage, manual focus/manual aperture lens adapted on a Canon EOS DSLR, you won't have any means of controlling the aperture via the camera's controls. You will have to set it using the lens' aperture ring. And, when you stop down you will see your viewfinder dim down, too. This is because there's no mechanical or electronic control over the aperture, maintaining it open until the moment of exposure (in the manner it would be if you were using it on an old Mamiya SLR).
The "chip", if the adapter has one, only provides limited assistance. Some of those chips are "programmable" so that the image EXIF will tell you what lens was used to make the image.... with a notation such as "50mm f/1.4". Usually this type chipped adapter comes with instructions. The EXIF doesn't reflect the actual aperture being used because it simply doesn't "know". There's no communication between the lens and the camera.
Perhaps the most useful thing the "chip" does is allow the camera's Focus Confirmation to work. To use it, you'll need to set the camera to One Shot focus mode while you still have an autofocus lens on the camera. Also select the AF point you want to work (might work with Zone or Small Zone, too... give it a try, I never have). The result is that Focus Confirmation will light up the LED when focus is achieved, which can be very helpful since it's difficult to focus visually since modern cameras, designed for autofocus lenses, don't have any of the manual focus assist features found in vintage cameras. If you have the Focus Confirmation "beep" enabled, it should work, too.
You can use the camera's Manual Exposure mode (M) and set the shutter speed, ISO and aperture (on the lens) using the camera's built in light meter. (With "match needle" technique.)
You also can use Aperture Priority Auto Exposure mode (Av)... set the ISO, select the aperture (on the lens) and let the camera select the shutter speed.
You probably can also use M with Auto ISO (which is actually another Auto Exposure mode). Here you set both the aperture (on the lens) and the shutter speed (on the camera), letting the camera choose the ISO.
DO NOT use Program AE (P) or Shutter Priority AE (Tv). Also do not use any of the "scene" modes (sports, landscape, portrait, etc.) and don't use full "Auto" or "CA" (Creative Auto). You simply cannot use any mode that requires the camera to set the aperture, which all of this will want to do.
There is a good article about adapting a variety of vintage lenses for use on Canon DSLRs here:
http://www.bobatkins.com/photography/eosfaq/manual_focus_EOS.html There are many different mounts that can be accommodated on the newer cameras, with the limitations noted above. The only caveat is, try to avoid the adapters that have to use "corrective" optics... as noted in the page above. The cheap optics in those adapters typically spoil the image quality of the lens, making it hardly worthwhile. In some cases, it's possible to remove the optics to maintain high image quality, but the lens will no longer be able to focus all the way to infinity (not a problem with some lenses.... but a deal killer with others). The same and even more vintage lenses can be adapted for use on the Canon M-series (APS-C) and R-series (full frame) mirrorless cameras.
On your 77D, with APS-C size sensor, that 55mm lens will "act like" a short telephoto lens. It will be very nice for portraiture, among other things.
AFAIK, none of the Mamiya M42 mount lenses used a stop-down lever (which was common on some early Pentax M42 lenses), so you probably simply set the f-stop on lens and it will actually close the aperture down when you do so. If you are using a small aperture (f/11, f/16) it will make your viewfinder very dim and difficult to use. Focus Confirmation may not get enough light to work, either. Try using the LCD on the rear of the camera in Live View and see if your camera has an "Exposure Preview", which can brighten up the image enough on that small screen to see to focus. It might also be possible to "zoom in" or magnify that preview, to more closely check manual focus. See your camera manual. These make working with an adapted vintage lens slower, but that may not be any problem for a lot of types of photography.