First and foremost I'm glad you decided to pick this game up!
Hmmm well it's kinda hard to describe the technique but I will do my best. The first clip (mausoleum) works a bit differently than the others as you just basically face the door sideways and aim and slide through. The rest all follow the same principle. Face the area you want to clip through, strafe back and forth while aiming until you get "sucked" into the object/wall. The key thing to remember is to let go of both analogs when you aim. I find if you hold down the analogs while trying to push through it won't work (or at the very least won't work AS well). The height of your aim/where you are aiming also matters. I usually try to aim straight ahead, maybe sometimes a bit lower but it all depends on the clip because some are more finicky than others. I'll do a brief run down of the clips.
Attic - so you actually don't NEED to do this one. Unless you get it pretty fast it saves minimal time. But it is worth learning if you want to save those precious seconds.
Into Penitentiary - series of 3 clips. First one through the gate is easy. Second one can be a pain sometimes. Third one through the dumpsters can also either be easy or hard. I tend to aim a bit lower for that one but that's just me.
Penitentiary Rage Quit - two clips, the first of which can be absolute hell (one time it took like 20 minutes because it stopped working). For the first one I always open the door on the left as you can see in my video. I find it makes it easier to clip through although some people don't do this (not sure if it even does help, I just found it easier imo). Then you just want to clip through on the left and kinda hope for the best. Most of the time you will get a "slow" pull which is better than nothing and other times you will get halfway in and then blocked so you'll have to retry. The second clip isn't too bad, just a really thin collision fence. You can clip anywhere through here but your location matters because if you land in the wrong place you will trigger a cutscene and get warped somewhere else where you will have to find your way back up to the fence and try again. Not sure where the trigger is but check out some videos for a rough location of where to perform the clip.
Church HELL - Last clip and also the hardest imo. Where you face the wall is very important here (at an angle). Getting in actually isn't too bad, the hardest part is what comes next. Now this is hard to explain, I would definitely check out a video for the exact details but once you are in you need to look to the left directly at that table thingy and a bit down. Most of the time you will get pushed back and have to try again but if done correctly you will push ahead and INTO the table. Just wiggle a bit until you drop down and find your way to the cave.
I'm terrible at explaining things but I hoped this somewhat helped at least. It took me quite a bit of time to be able to do some of these clips a bit consistently but don't be discouraged. There is a big RNG/randomness factor to it as well sometimes.
If you have any more questions or anything specific you want to ask feel free. Good luck!
Yeah you never want to press any analogs at any point in time other than strafing in front of the wall you want to clip. As for the quick strafing thing uh that is hard to explain, I never really noticed. There must be a rhythm or something where you can do it faster but I'm not even sure how to explain how to do it.