You can explore each system, survey planets and also conduct archaeological digs. If a planet is suitable you may colonize it.
To expand you will need outposts and colonies. Outposts can extend the range of your fleets without requiring the investment of a colony. You can only colonize planets if they have a suitable environment for your people.
Moving task forces: To order a move, select a task force on the task force panel and then click the destination sub-sector on the map. A line will be plotted indicating the movement order has been set.
Surveying a system: To do a thorough examination of a system, you can order a task force to survey a system or planet. Click a task force on the task force panel and then hover over the orders button and click survey. Then on the sector panel, select a planet or the star to survey all planets.
Digging for discoveries: You can order a dig if you think a planet may contain hidden artifacts. Digs are usually done after a survey reveals something hidden on the planet or if you have other information. To order a dig click, a task force on the task force panel, select it’s order and then pick a planet in the sector panel.