I was recently approved for a service related disability. How do I get my id card ?

It sounds like you're asking about applying for the Veterans Health Identification Card (VHIC). The difference between the VHIC and the VIC (Veteran ID Card) is that the VHIC will confirm your eligibility status (in your case, "service connected") and will allow access to military bases, MWR facilities, etc. that are open to disabled veterans.

If you haven't already, enroll online* with VA health care (there is no cost to enroll), as that is a requirement to apply for a VHIC. After you are enrolled (not just 'submitted' - confirmed enrollment), then you can apply online or in-person for the VHIC*.
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* Online application for VA health care - https://www.va.gov/health-care/how-to-apply/
* Apply for a VHIC - https://www.va.gov/health-care/get-health-id-card/

For a VA Id card go here for info: https://www.va.gov/records/get-veteran-id-cards/vic/

If you were rated at 100% or TDIU you would take your award letter to a RAPIDS office to get a DoD ID card.