There are 3 ways to get an equity card.
1. They have what is basically a points system. Work 50 (I believe) week as a non equity preformer in an equity production, and you get one point for each week. You are then elligable. Points can be accumulated in multiple productions.
2. Get hired as while you are non equity for a production that needs a certain percent of equity actors. It is possible to be offered papers on the spot which can be signed for your equity card.
3. If you are a member of another preformance related/based union, SAG for example, you can automatically get an equity card.
"We don't value the lily less for not being made of flint and built to last. Life's bounty is in it's flow, later is too late. Where is the song when it's been sung, the dance when it's been danced? It's only we humans who want to own the future too."
- Tom Stoppard, Shipwreck