I just read a wonderful blog post by my favorite film critique and soon to be Deacon, Mr. Steven D. Greydanus. The post is in regards to the Lord's day and the third commandment and how we as a people can keep it holy. It's certainly a very important topic and will be different for each family and each person but I thought I'd share my thoughts on the subject and how our family has been striving to fulfil this 'day of rest' commandment.
The most obvious way of observing the Sabbath is the Sunday Mass. The obligation to attend Mass on Sunday is binding and should only be missed due to absolute necessity (sickness, etc). Again the church explains it clearly in Canon 1247 (LINK). Prepping for this by reading the scriptures ahead of time and listening and reading additional commentaries are also very helpful, but what helps us the most is discussing the readings and the homily after Mass as a family.
Secondly, we do not do any shopping on the Lord's Day. This was difficult at first but now it's a breeze and a joy. By doing this we hope to somehow influence the culture that says that every day of the week is a work day. It's especially a tough message on workers who are paid hourly who are forced to work every day possible even if we have the divine commandment to not work during that day. There are of course occupations (doctors, policemen, etc) that must work on Sunday (as the Catechism describes in Paragraph 2185 (LINK)), but for most of us we should strive to not only keep the sabbath holy for ourselves, but also give others the opportunity to do the same. That's one of the reasons we really like supporting Chick-Fil-A which is probably the only major fast food restaurant that has always been closed on Sundays (it also is AMAZING for kids - food wise, price wise, kids meal toy wise, and exercise wise).
We try to get all of the housework and weekend shopping done on Saturday or other days of the week. Not working on the Lord's Day helps us to connect with family, enjoy our time together, get to know each other more, and generally not fret and flurry about like Martha in the Gospel passage.
Finally, a third way in which we as a family observe the sabbath that is probably fairly unique is we try to observe a 'No Power Hour' on Sundays. We chose the hour of divine mercy (3pm-4pm). What we do is literally shut off the circuit breaker of our house and turn off all wireless devices (phones and laptops). It's incredibly peaceful and serene. No hum of the refrigerator, heater, dryer, etc. Just family time. A lot of times we'll just go for a walk. It's also generally light enough to still be able to play in the house or read. Also the kids are sometimes still taking their nap at this time. We're certainly not 100% on this tradition yet but we have done it many times and really like it. It brings us closer to the Lord and closer to each other. It also gives us a sense of solidarity with our ancestors who did not have access to power and internet and helps us realize what a blessed time we live in.
Those are just a couple things I can think of. Feel free to share your thoughts and ideas!