This problem can be multi-faceted. Someone could guess all day long as to what the problem(s) is / are and not even come close. Air conditioning isn't something to guess at. It's like having a rattle on a car and taking the approach of replacing one part at a time to find the rattle. It would be cheaper to just buy a new car. ( I give that as an example you can easily understand. You probably won't like it but the truth is always hard to swallow when it involves money.)
This is why air conditioning is a billion dollar plus industry. It's unlikely you will solve this kind of problem on your own as a "do it yourself" solution.
Sure you can do the things suggested like window coverings but if the problem is a "system performance" problem it's unlikely to make much difference.
With all of this said... if the problem isn't found and corrected it is quite possible to spend all kinds of money wastefully. The air conditioning business isn't known for being "easy". Certainly some repairs can be but issues such as these can be quite difficult.
It's quite possible it's just too hot. If out door temps are up over 110 degrees and you're hitting 76 inside... well if you think the AC is not working go outside for 15 minutes or so and walk back in. That dial on the wall is to turn the unit on and attempt to hit the desired temperature that you set. But there is no guarantee that it will. Air conditioning (depending on climate, location and design of the system) is mostly designed to lower the temperature 20 degrees from that of outside. (again this depends upon design of the system.)
Air conditioning loses noticeable capacity at 105 degree outdoor temp. again depending on climate and design of the system. Air conditioning isn't a cookie cutter appliance. One size does not fit all.
If out door temps hit 110 or more, be happy with what you get and reduce indoor loads. Plasma TV's, specialize computer equipment, excessive incandescent lighting, halogen lighting, excessive people loads (more than two per room), etc. will only add to your discomfort.
I am a licensed HVAC contractor with over 20 years experience in Residential HVAC systems. Serving the Katy & Cypress Texas area (suburb of Houston)