It's been 40 years since I've had my hands on a marine radar, so no doubt much of what I'm going to talk about here is probably out of date. Modern radars probably have all sorts of automatic functions to solve ETA and CPA solutions by just the press of a button, but there is also an old-fashioned way of doing it, too, which you can practice at home. I was trained to do radar navigation with a maneuvering board, which is not a "board" at all, but a 12"x12" pre-printed paper form with a compass rose and concentric range rings on it used to solve relative motion problems. You can see what they look like by Googling "maneuvering board" on the net, and you can buy them at many chandleries, or order them from marine supply houses. You've probably seen them in movies about the Navy, where they always show a sailor in headphones standing in front of a huge glass maneuvering board in the ship's Combat Information Center writing down the motions of enemy bandits backwards with grease pencil. MBs can also be used as universal plotting sheets (which they closely resemble) for celestial navigation purposes.
The standard maneuvering board has a 10" compass rose printed on both sides, along with 10 concentric rings arranged like a target around the center. This allows you to plot the bearing and range to a target on the board, and to continue plotting it as it changes over time. This may seem rather pointless, but if you are traveling in the dark and there are several radar echoes scattered about you, some stationary and some in motion, keeping track of them in order to avoid a collision can be quite challenging. The board allows you to determine "closest point of approach" and "estimated time of arrival" solutions, and to predict the bearing and range to a target at any time. It can also be useful to change and maintain station in formation, launching torpedoes, intercepting or avoiding enemy shipping, and a variety of other tasks which you may not be doing too much of in your ComPac, but is still fun to play with . And remember, if you really understand all these maneuvers, you can use your radar and its automated features more effectively. We used to call failures to properly interpret radar displays as "radar assisted collisions" . Maritime history is full of examples of shipwreck and loss of life between ships equipped with the latest radar technology. Machines don't lie, but sailors can screw up. You have been warned. Maneuvering boards can also be used to solve current and leeway problems, and calculating true and relative wind. They also have a nomogram printed on them, a handy scale that allows you to solve time-speed-distance problems by just laying a straight edge across two and reading the answer off the third.
Googling "maneuvering board" immediately will take you to several websites where you can download detailed instructions and tutorials on their use, but I will give you a taste of it here and try to whet your appetite. There is also a chapter in Dutton's devoted to the Board. BTW, Dutton's "Navigation and Piloting" is far superior to Chapman's "Seamanship and Small Boat Handling". I highly recommend it.
The Geographic Plot
This is the simplest, and least used plotting technique, but I will mention it here because it is the easiest to understand. Plot your ship's course on the board, starting off from the center, and mark off distances at time intervals where you ping your target on radar. If your target is stationary, like a buoy, your bearings will all converge on the same spot, it's position. If your target is also in motion, you will have a map of its course and yours.
The Relative Plot
In Relative Plotting, your ship is always at the center of the board, regardless of its course and speed. As you periodically ping your target with radar or visually, its range and bearing are plotted on the chart relative to your ship, not the ground. I.e., the relative motion of the target on the board contains information on its course and speed as well as yours. This allows you to determine if there is a danger of collision, and how to maneuver if there is. It allows you to calculate closest point of approach, as well as the time, bearing and range of the target at CPA. I remember one night sailing on a Bristol Channel Cutter 28 through Southern California's Channel Islands where the captain was below, glued to his radar doing this, while I had the helm and followed up on his radar contacts with binoculars, confirming that their running lights agreed with our predictions of their motion.
Avoiding another boat is easy, avoiding a dozen of them at different distances, courses, and speeds in crowded waters when all they show is a light, can be quite a challenge. In a fog it could be critical. Those other contacts may be big ships, not as free to maneuver as your yacht.
In addition to plotting, a maneuvering board can also be used as a computer to graphically solve vector additions and subtractions. You can convert from true to relative motion and back, Intercept or Avoidance maneuvers, correcting for wind, leeway, current set and drift, and of course, computing torpedo solutions. You never know when that might come in handy.