While you could just run around and hope you stumble upon a base, there's a much more efficient method of locating your enemies. You can do that by tracking.
There are two different types of trackers: permanent and temporary. Permanent trackers consist of a diamond block, obsidian, and a gold block for the tips. A temporary tracker consist of an obsidian block, cobblestone, and smooth stone for the tips.
Top: Temporary Tracker Bottom: Permanent Tracker
Each block on the tracker adds 25 blocks to track the player. You can make the tracker as large as you'd like, there's no limit.
The trackers don't have to have the same size legs. This one tracks 25, 75, 200, and 275 in different directions.
Although temporary trackers are cheaper to make, they can only be used one time. Once you use them, they disappear. Also, temporary trackers can only be used to track one specific player (/track
To track someone, you'll need them on two different directions (Only having one won't help you much). Since each block on the tracker is 25 blocks, you'll want to narrow it in to about 25x25. You can do this on a permanent tracker by moving the gold blocks in.
You can see that moving the gold block in lowers the tracking region.
Good luck and happy raiding!