`/run` should be world-accessible, and only writable by root.
chmod 755 /run
However, you may run into more trouble, since whatever caused `/run` to have wrong permissions may have affected other files. There is no generic way to fix such problems. It depends on what happened. Maybe one of the previous questions on similar problems will be relevant to you.
If _only_ `/run` and its contents is affected, just reboot: `/run` is an in-memory filesystem and is recreated from scratch at each boot. On the other hand, if other parts of the system are affected, it may be better to repair what you can before rebooting, since the system may have become unbootable.