Back story, been riding and racing since 92 and I have literally never done any stretching, foam rolling or had a massage.
I’m starting to feel tight in the hips and my legs feel like they are made of rock.
I’ve spent a bit of time researching various exercises to do but some of them I’m just not flexible enough to even attempt.
What’s good to get me started and when should I do them.
I cant recommend ROMWOD enough. Im sure you can guess by the name, but its got a strong CrossFit pull- which is still good for cyclist, as it focuses on athletes.
Its a yin-yoga based app, $10 or $12 a month and quick, 20 minute sessions you can do before bed. Yin is a style of yoga where you hold poses longer and help open joints up. Most poses specifically focus on the hips.
Following this thread since I’m in the same boat of being laughably inflexible.
I just started doing the Sufferfest’s yoga/stretching plan about a week ago - little 15 minute videos (I think the person who does them, Abi Carver, also has a standalone site). So far, it seems pretty decent.
Not to be a party pooper, but I’ve read that you can’t actually stretch any of your body parts; your hamstrings being one of the very few which can be technically lengthened. It’s more about your brain than your body.
That said, I do a lot of “stretching” for hips and hamstrings. General sport stretching is a good place to start; move into yoga poses once you think you are flexible…you’ll quickly find out you are not flexible! 
Agreed, from what I’ve seen it’s less about the muscle or tendons being “short” as it is your brain being protective and preventing lengthening to stop you from hurting yourself. So stretching is less about making things longer as it is about teaching your brain that you aren’t going to hurt yourself in different positions so that it lets you get there. I’ve read that not matter how inflexible you might be, if you are knocked out or given anesthesia then someone can basically put your body into positions that would make cirque du soleil performers jealous.
One of the best things that I have found for increasing range of motion is longer (30+ second) stretches with deep breathing. On each exhale you try to fall a little bit deeper into the stretch.
EDIT: It is as much about relaxing as anything. A stretching session might be lightly physically strenuous but mentally it should be as relaxing as possible. It may be different for you and may take some time to get here but about 15-30 seconds into a stretch I usually feel my muscles “give in” to the stretch and sort of “fall” into it. But you need to be relaxed and go slowly so your brain’s protective mechanisms don’t kick in.
I’m a huge fan boy of Kelly Starrett and The Ready State. He has both Facebook and Instagram quick stuff daily along with subscription based mobility work. https://thereadystate.com/ He’s been on the podcast I believe and is an amazing athlete not just a guy that knows how to do stuff. Try his 10 minute squat test and you’ll see how tight your hips really are.
To further the suggestion above, he became well known by putting out a video a day. A PT friend of mine got me started on them years ago, and you’ll learn a lot and feel a lot better. Just do one or a few a day. I think it’s worth it to do them in order, but then also find others down the list to address what’s specifically bothering you that day. This is the list of them:
Things just pop up in the right time Kelly’s YouTube today is cycling specific. Improve Cycling Efficiency - YouTube
I’m a big fan of Kelly Starrett as well but with the amount of content he puts out can be a little overwhelming until you know what you like/want to focus on. A few years ago a friend told me about this youtube channel as I was talking about how I felt like yoga would be beneficial but I hate doing it. Erin’s routines are short, not stereotypical spiritual yoga stuff (not my thing) with plenty of modifications if you’re not flexible. Here’s her beginner hip and hamstring routine:
Most of her stuff is pretty good- some of the core-focused routines are killer. I try to do at least 1-2 a week (more in the off season) and have definitely noticed a difference in my overall posture in addition to feeling a bit better on the bike.
Chek out Athletes for Yoga: https://video.athletesforyoga.com
It’s the old platform from jasyoga moved into a new concept. lots of specific stuff for cyclists and triathletes, pre/post workout stuff ~5min as well as specific resets for hips/hamstrings etc etc (~5min routines)
There’s an interview with Erin Taylor on the purple patch podcast