I attend a small Reconstructionist synagogue in Northern California. We are not able to afford to pay our Rabbi full time so we have Friday night services twice a month and Saturday morning services once a month, plus a Friday night chant circle (think Shefa Gold), the occasional B'nai Mitzvah, and various other events.
Friday night: Tonight we will attend services (not sundown yet here), which we drive to, as does almost everyone there. They last about 2 hours and include a lot of singing, chanting, and speaking of prayers in both English and Hebrew. The Rabbi gives a drosh (which are always wonderful). Our siddurim have both languages plus transliteration. Everything is 100% egalitarian.
The service starts with candle lighting. After the service we go into what we call the oneg room for a kiddish (we just call it oneg). A light buffet dinner provided by whatever person/family volunteered that week. We pray over the wine (with grape juice and water for kids and non-drinkers) and then the bread. Then we eat and chat.
If we're home Friday night, we light shabbat candles and have a sit down dinner. I don't know what most of my fellow congregants do regularly but at least some weeks we all try to make Friday night dinner special, and sometimes get together with others (sometimes we have a potluck dinner at shul).
Saturday morning, if there is a service we drive to shul and attend. We wear talliot (tallism? I often mix the Yiddish with the Hebrew) and bring out the Torah for a reading or 3. We do not have designated readings and do not make any distinction between someone who is a Cohen or Levite vs not, though readers are chosen in advance so they can practice. We have a full service that runs about 2 hours, along with the usual singing, etc. We sometimes do Storahtelling or have a drosh, but those are usually for special occasions. People who have had a B'nai Mitzvah can sometimes lead a service and we have guest leaders too (also on Fridays). Saturday morning services are also followed by a kiddish, or at least the wine.
Occasionally, our shul will have a Saturday night service for Havdalah. I admit we rarely do that at home, though we have all the materials. And of course we have services for various holidays, not just High Holy Days, plus other holiday events (a Passover seder, a Chanukah party, late night Shavuot study) throughout the year.
People differ greatly on what they do and don't do on Shabbat. The shul's board and other leadership do not do shul business on Shabbat. Many congregants do not do their usual work on Shabbat, or at least try not to (not everyone gets to pick their schedules).
Some people try to make Shabbat family time and go for walks or play games that aren't electronic. Some try to do some Torah study or other religious study. Some families with young children get together to do outdoor activities, weather permitting.
Most of the prohibitions just aren't part of our lives though. I don't know anyone aside from Orthodox friends/family who won't drive, use electricity, cook, etc. Two Conservative Rabbis I know will not write on Shabbat, but I don't know anyone Reconstructionist who doesn't write. Setting the day aside as "different" is common, but we are not frum.