how do i repair disk permissions

You repair permissions with the Disk Utility in the /Applications/Utilities/ folder as before.

You repair disk by starting up with the Option key held down and specifying Lion's recovery drive. The procedure is otherwise identical with that in Mac OS X 10.6.8 and earlier.

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As Neil points out, in general there are two different repair options: the permissions or the disk itself.

For the permissions (left set of buttons), the only requisite is that you run Disk Utility using an Administrator account. So you start DU up, select the appropriate VOLUME on the left column (i.e. "Macintosh HD") so it is highlighted and click on the Repair Disk Permissions button, then wait awhile till it finishes.

For repairing the disk itself, you need to boot off the Recovery Drive, either by holding down the Option key before the startup chime and selecting the recovery icon from the list presented, or by holding down Command-R before the startup chime. Note that most recent Macs will attempt to start up via Internet Recovery with this option and may take awhile to start. Once the recovery system is up and running, start the Disk Utility via the menu option in order to do the Repair Disk task. (For more info on Lion Recovery, see here: http://www.apple.com/macosx/recovery/ )

Note that Lion offers two different Repair Disk subtasks: repair the device or repair the volume. If you select the device by highlighting it (i.e., xxxGB Apple HDD...) and clicking on Repair Disk, the partitions are verified and repaired as needed, whereas if you select the volume(s) instead (i.e., Macintosh HD) and do the Repair Disk, the volume structure gets repaired. I recommend you do both.