Sounds like an oxymoron, doesn't? Sabbath work? Is Sabbath a time to rest, or isn't it?
We see in the book of Acts how the early church, the very first Christians, used the Sabbath time to do the work of Jesus. The first Christ-followers were devout Jews who never missed synagogue on the Sabbath day. It was a time to cease earthly labors, but liturgy (the work of the people), that is, worship, was entirely appropriate and expected. A part of worship was to deliver teaching on the scriptures.
When a very learned man like Paul was a guest in a synagogue, the leaders invited him to speak. Thus, we see him in Acts 13 (especially verses 14 & 44), in the synagogue accepting the invitation to speak. And, in that context, he spoke of Jesus - how Jesus was the fulfillment of the Hebrew scriptures (what Christians today refer to as the Old Testament). His desire, more than being a good sabbath-keeper, was to help people put their faith in Jesus Christ.
How do we follow Paul's example today, and do the work of sharing Jesus even when we are on Sabbath time?
First, we worship. Paul didn't have a secret strategy to"win over" the Jews. He went to synagogue with pure motives. It was Sabbath and that's what they did. Today, whatever we have in mind for when and how we keep Sabbath time, it must include worship. And whether or not we keep our Sabbath time on Sunday, we need to be in church with our church family worshiping God together. Like Paul, we must worship with the body of believers.
Second, we have to be ready to share Christ at all times. That means we spend our lives immersed in the Gospels and the New Testament, so we have ingrained in us the truth about Jesus. We're ready with a message: God loves us so much that he sent his son Jesus to die for our sins and whoever believes in him shall not die (in sin) but shall have eternal life. At all times (including on Sabbath, including in worship) we stay ready to share the good news.
Third, we don't just cram it down people's throats. "The people begged that these matters [the truth about Jesus as fulfillment of the scriptures] be presented to them the following Sabbath" (Acts 13:42). Paul didn't have to be tricky. The people begged him to share the goodnews. Likewise, we share our faith in the context of relationships with others. We share when it is clear the person we're with is ready and willing and interested in hearing us. In Athens, among gentiles, Paul said nothing about Jewish law, but rather shared Christ in ways intelligible to the people there (Acts 17:18-34). We share Jesus in terms the other will understand.
So to review, the works of the Sabbath are worship and evangelism. The worship is with the community of faith. The evangelism is with people who are willing and done in a way that they will understand the message.
These works are appropriate and required at other times as well. Any time is right for these works of faith, and the Sabbath is no time to stop worshiping and testifying to the good news. In our rest, our time shared together and our play, we praise God and share how wonderful He is that others might join us in praising and loving Him.