Let's get the bad news out of the way upfront: I don't have any simple answers that will make docking in current easy, and neither does anyone else.
It's just one of those cruising tasks that's damned difficult to do well, bundled with a heaping helping of boat damage risk.
What I can do is explain the theory and then provide some examples of how to apply it.
Not only will this understanding help us get docked safely in current, it will enable us to determine when a situation is not going to end well, no matter what we do.
Knowing when to fold 'em is one of the most important, and yet under-rated, seamanship skills, not an admission of failure. Or, to put it another way, anyone who says "I can dock in any situation in any conditions" or anything like that, is a dangerous idiot, not someone to be admired.
Before we go any further, please make sure you have read the rest of this Online Book and maybe reread it if it's been a while.
If you don't clearly understand prop walk, prop wash, turn sidle, and what a magic spring is and how to use it, none of what follows is going to make a bit of sense.
With that out of the way, here's the vital tip that makes docking in current easier: