After getting approved for the IRR, what steps should I take next?

During this time you should work on your education and take advantage of completing online military courses. No one knows what the future holds so do your best to stay at the top of your game. CW3 (Join to see)

Depends. What do you WANT to do?
All you are REQUIRED to do is keep your contact info up to date and report if there is an IRR muster. It is a great place to hang out if you are looking for tours. Lots of flexibility.

A more break down:

An individual assigned to the IRR typically receives no pay and is not obligated to drill, conduct annual training, or participate in any military activities (except for periodic Muster activities) until activated by Presidential Reserve Callup Authority or until electing to drill, train, or serve in a "Drill without Pay" or an "Active Duty" role. Unlike members of the Standby Reserve (active and inactive) and Retired Reserve, IRR personnel are members of the Ready Reserve and as such, they retain their status as uniformed military personnel, their military specialty (i.e., pilot, Surface Warfare Officer, infantryman, intelligence officer or enlisted intelligence specialist, etc.) and rank/pay grade. IRR personnel also receive benefits similar to other members of the Reserve Components of the Armed Forces to include: Entitlement to a Military ID Card, ID Cards for their dependents, PX/BX/NEX/MCX/CGX (Exchange) benefits, Commissary benefits, and MWR (Morale Welfare and Recreation) Benefits. (Note: These benefits are only available to IRR Members in the "CONUS" 48 States.) An individual assigned to the IRR may receive pay and full benefits (including medical care and dental care for member and dependents) for voluntarily performing specific types of active duty. Because members of the IRR rarely serve on extended active duty and are not retired from military service most are not eligible for TRICARE. However, if honorably discharged, they do have the VA for medical benefits.[1]

By law, IRR members are required to retain possession of their service uniforms, retain their military identification card, and notify their service branch if they move and change their address.

Upon being called up, service members will usually be screened for their medical and personal status in order to qualify or disqualify them for activation. During the process, IRR members who seek to delay, defer, or exempt their activations have the opportunity to present their case to the mobilization authority for a decision.

An enlisted service member's IRR service ends after the completion of their mandatory service obligation (MSO), usually 8 years.

The Individual Ready Reserve, Selected Reserve, and Inactive National Guard comprise the three Ready Reserve programs.