The Short Answer: Ask God.
The Long Answer: Mormons make up a lot of little rules, and this isn't always a bad thing. They're personal commandments they follow so they can obey Jesus Christ more exactly. For instance, a lot of Mormons don't drink caffeine. The Word of Wisdom says not to have hot drinks, or Coffee and Tea. It doesn't say not to consume caffeine, but to keep from being addicted to anything, a lot of Mormons don't drink caffeinated drinks. At the same time, plenty of Mormons enjoy their Diet Coke. It's really a matter to discuss with the Lord.
In the same vein are the "Mormon Prohibited Sunday Activities:" working, shopping, housework, sports, movies, etc. The list can go on. Anything that can be done on any other day of the week and that could detract from the Spirit should be avoided. Of course, sometimes you have to go into work one Sunday, or your kid has a cold so you have to run into the store and grab some cough syrup. These situations are understandable, but they shouldn't become habits. Try as best as you can to not work on Sundays. At the very least, try to make it to church.
The better question to ask is, "What should I do on Sundays?" Go to church, visit your family, visit the sick or elderly, do service, go to a fireside, study the scriptures, watch an uplifting movie, etc. Anything that will help you remember our Savior and feel closer to the Spirit. There are many blessings that come from keeping the Sabbath Day holy, and we want you to fully enjoy all of them.
What are some good Sabbath Day activities you enjoy?