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.
This Shibashi 18 set Taiji Qigong video is by Master Wing Cheung
This Shibashi 18 set Taiji Qigong video is by Shan-Tung Hsu's Hong Kong 'sister'.
(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)
(...she has trained for many years, so don't let her great flexibility put you off)
'Tai Chi for Arthritis' form by Dr Paul Lam:
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.
...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 28th April 2018