Time Machine automatically deletes your oldest backups as you create new ones as space is needed, but you might encounter an issue where you connect your Time Machine drive only to be told that Time Machine could not complete the backup because your backup is too large for the backup disk.
In such an instance, it's time to take action and manually delete some of your older Time Machine restore points. There are two ways to do this: through the Time Machine app itself or via Finder. Either way, you'll need to connect your Time Machine drive to your Mac before proceeding. So, go grab that; I'll wait right here.
OK, with your Time Machine drive connected, let's get to work.
Method 1: Via Time Machine
This is the preferred method, since it's faster. Using Finder, (in the next method) you move a backup folder to the trash, and it takes a long time to empty the trash when it contains a Time Machine backup. Here's how to do it through the app:
1. With your Time Machine drive connected, click its menu bar icon and choose Enter Time Machine. (If you don't see the icon, go to System Preferences > Time Machine and check the box for Show Time Machine in menu bar.)
2. Navigate to the backup you want to delete, click the gear icon button and select Delete Backup. (Alternatively, you can right-click within the Finder window for a backup in Time Machine and select Delete Backup.)
3. Click OK to confirm you want to permanently remove the selected backup.
4. Enter your system password when asked.
5. Click Cancel to exit Time Machine and delete the backup.
(Strangely, Time Machine just sits there after you enter your password and makes you hit Cancel to move things along. But that's the odd, final step.)
Method 2: Via Finder (and the Trash)
1. With your Time Machine drive connected, open Finder and click Time Machine in the left panel.
2. In the Backups.backupdb folder, you'll find dated folders of your backups. Right-click on the folder you want to delete and choose Move to Trash.
3. Right-click on the Trash in the Dock and choose Empty Trash.
4. Wait a long time for the Trash to be emptied.