Give me 10 days...
I used to teach ball golf and maybe this will help. What edge3281 said about starting at 5 ft is really a big deal. Yes, it seems to be silly at first, but it has a skill/confidence building advantage. I'll explain in a second.
What style to putt in. There are tons of ways, but here is a suggestion. Why not use the same stance as you use with your approach shots? If your game is solid, go with what works for you. (When teaching ball golf, I was huge in saying forget what the books say, you should adapt with what is already working for you and build from that. There are some real ugly swings in the pro tour, but they play as good as the pretty ones.) SO go with what is simple and comfortable. Also, I would use the same style and brand of putter. Again find one that is comfortable. Don't keep changing weights and styles. That will get you thinking about that stuff instead of making the putts.
Next, if you want to make putts you need a pre-putt routine. Come up with one of your own that you WILL do before EVERY putt. I personally never step up to the putt until I am ready to just throw it. I sit back look at the link I want to hit and imagine myself throwing the disc and hitting that link (I do this until I REALLY see it work). Then all I do is step into my stance point the edge of the disc at that link pull back and throw. I also make myself leave my hand out there like I am shaking hands with that link until the disc hits (it forces the aim and "the memory" of the aim).
The reason I do this stuff in this manner is so I get all that thinking out of the way before I am ready to throw (I even do this while others are putting). This way when you step into your stance you just aim and putt and there is no time to allow extra thinking to get into your head. If you see it in your mind your body naturally wants to copy it. That is how are brains are wired (this has been scientifically proven many times).
Now to practice this starting at 5 ft. Why start there? It is because you can't miss those. It is all about confidence. You MUST do your pre-shot routine for every putt (that means not standing in your stance at the spot you will be throwing before each throw) and do 5 putts at 5 ft. Then take 2 steps back and do it again and then 2 steps back and do it again and just keep going. You MUST complete all 5 throws at each spot. If miss 1 of the 5 start over (but finish all 5 throws no matter how many you missed). If you did not do the pre-shot routine on one putt, that counts as MISS. We are training your mental side as well as your physical side. In putting it is debated but at the very least a 50/50 ratio of the two. So both must be trained to improve.
When (and you WILL!) you get to where the 10 ft putt is a can't miss, then start there and forget the 5 ft starting point (BUT you have to be sure that 10 ft is easy before doing that.) I personally will never start from further than 10 ft, because that is the confidence building distance.
Do this for your 30 minutes a day from that video or until you have gone through it at least 3 times as far as you can. In just 10 days of this, 15 ft putts will feel like 'gimmies' for you.
This sure took a long time to write up, but it is worth it for me to see written out as it was to share it. Now your job is to teach me to drive better as my approach and putting is all I am good at.