Youtube is a great resource, but there are also plenty of poor or inappropriate examples of Tai Chi on there (you don't have to be an expert to post a clip online), so check the feedback before trusting any videos.
Training with an Instructor is the best way to ensure you are performing the moves safely for you, especially if you have an existing health condition; but here are a few useful videos in the meantime.
1st video is Prof. Lin Housheng, who created the Shibashi 18 movements/steps/form system in 1979, filmed here in 1984. (Repeat each move 6 times)
www.youtube.com/watch?v=Master Lin Housheng
2nd video is Master Wing Cheung's gentle version of this Shibashi 18
www.youtube.com/watch?v=Master Wing Cheung
3rd video is Hong Kong's 'sister' Shan-Tung Hsu's version of Shibashi 18
(Chinese with English descriptions. 1st 20 mins = breakdown, 2nd 20mins = flowing movements)
The "Lady in Pink" is well known for the simplified 24 form (the most popular across the world)
Don't let her great flexibility put you off ~ Gao Jiamin is a 32 times gold medal winner
Here is Erle Montaigue's Yang-style Cheng-fu Taijiquan / Tai Chi 108 long form
This Sun-style 'Tai Chi for Arthritis' form was created by Dr Paul Lam in 1996:
www.youtube.com/watch?v=Tai Chi for Arthritis
Here is a 50 min talk by Dr Paul Lam on his "Tai Chi for Health Program" clearly a fit 60+ year old in 2009 despite being an Arthritis sufferer from the age of 13.
www.youtube.com/watch?v=Dr Paul Lam
...BBC's Trust Me, I'm a Doctor, said Tai Chi was "as good for you as Zumba":
World Tai Chi & Qigong Day photos from Sat 27th April 2019
click on image for photos