The new program is completely digital so there's no membership card to carry around. You just need to provide the phone number attached to the account when you pay.
If you're wondering how long it'll take you to save enough points for that free entree, you get 500 points for signing up for the program and then 10 points for every $1 spent, so you're looking at spending $50 before you get the first free entree. Similar to Starbucks' reward program, there are also occasional bonus point opportunities.
You can enroll in My Wei Rewards at http://PeiWei.com/MyWei or by texting MYWEI to 242-647.