I'm looking for some good tutorials, tips or advice on how to increase my flexibility.
Clearly stretching regularly and high water intake helps but I'm wondering what else I can do to improve my flexibility, particularly in my core and back.
As someone who is pretty stiff and has been looking at improving his flexibility for a while I can probably help you out a bit.
To give you my background and some hope, I am a sporty person since I am 7 years old. I have always been quite active since then (competition in track & field, ...) and am now 29 years old. Yet, flexibility has never been my focus and has never been my strength. It became a problem when I started doing weightlifting: it hit my face pretty hard that i was not able to perform some movements because of a lack of flexibility. So I searched a solution.
The effective solution I found (I really improved my mobility significantly) is the following :
First and foremost, understand that the goal of stretching is to make your Central Nervous System (CNS) understand that a new Range Of Movement (ROM) is desirable and safe. It has (to my belief) nothing to do with actually lengthening the muscle. Old beliefs said so. New research suggests the adaptations are mostly neurological. Apparently, if you put yourself under general anaesthesia i.e. remove your CNS from the equation, you shall be able to do a full split without any issue. Once you understand and accept that, then you will also understand the proper techniques to gain flexibility and mobility
Second, incorporate daily flexibility work wherever you can e.g. reach overhead, reach at your feet, squat, ... Do as much as possible the movements you want to achieve and avoid sitting for extended periods of time. When at home, try incorporating mobility work when watching TVs, playing games, playing with your kids, ... Recognize that you need to move more. Except if you are a pro athlete, 1h of daily activity does not (unfortunately) undo 8 hours+ of sitting (office, car, plane, sofa, ...)
Third, do one (or more if you can support it) dedicated flexibility training a week with proper focus on breathing and using PNF techniques (google that if needed). Proper breathing i.e. belly breathing is essential since (see first point) flexibility is mainly associated to neurological adaptations i.e. making your body understand that a new ROM is safe. This is achieved by proper breathing which allows you connecting with your CNS and telling him "this ROM is safe, go there" PNF techniques allow you to use body reflexes to increase your improvements rapidly. Also if you can, stretch with a partner. This allows you to get deeper stretching and to relax more since the partner helps you get into the position i.e. you use less tension and it is highly beneficial to get the desired adaptations. Stretching using weights can also be very useful e.g. goblet squat to improve squat depth, loaded shoulder flexion. Just make sure you have a proper movement pattern and you are correctly mobilising your joints. A coach, an educated friend or peer review (post a video on reddit asking for form assessment) can be of help.
The resources I would recommend are MobilityWod from K.Starret (soft tissue and banded distractions, The Roll Model from Jill Miller (lot on breathing) and Stretch Therapy from Kit Laughlin. From there and with this knowledge, you shall be able to fine tune your own routine, learn advanced techniques and navigate through the many youtube videos on the subject.
Hope this helps !