My "process" is that I break down the combo into it's base parts, then I focus on performing those parts separate if I can. The most basic example is SFIV's Ryu.
cr.HP xx Shoryuken FADC Ultra I
Learning cr.HP cancelled into Shoryuken is easy enough. Just input Shoryuken before the cr.HP connects and they'll lovingly combo together for good damage.
The problem is inputting that, then doing the Focus Attack Dash Cancel using MP+MK together (Immediately after inputting Shoryuken), then dashing forward with "Forward, Forward", then inputting QCFx2+PPP in time to connect the Ultra.
So what do you do to get this down to muscle memory?
Practice doing the Ultra motion.
Practice Dashing and doing Ultra.
Practice holding Focus Attack, Dashing, then doing the Ultra.
Practice Shoryuken into Focus Attack Cancel
Practice Shoryuken into Focus Attack Cancel and Dashing.
Practice cr.HP xx Shoryuken Focus Attack Cancel and Dashing.
Practice cr.HP xx Shoryuken FADC Ultra I
Practice substituting cr.HP with more appropriate strings as necessary.
Once you have that down pat, all similar combinations are really easy to do, and motions like these are prevalent in a number of titles, so time isn't truly wasted when jumping over to another game. Things like SFIV combos are cakewalk to memorize, but longer combos like those found in BlazBlue are easy enough to memorize through the same process. The motions you're turning into muscle memory are simply combinations of button inputs as opposed to one movement and one button.
I would practice those in the same fashion. Break the combo down into parts I can remember, practice those separate parts until I understand them, then work them into muscle memory as one longer combo.
https://www.youtube.com/watch?v=ceB9KPnfhnQ
This is one I practiced by starting with the first five or so hits, and slowly adding onto it as I went. I also practiced simpler versions that were easier to time, so I could practice the timing for the ending "loops", before moving onto more damaging versions that involved a lot of extra hits.