How to "practice" acceptance
Acceptance is a result of practice, not something you do. You could say it's something that happens. Some things you already accept automatically; some things you accept after some resistance; some you don't accept at all, because you don't realize that non-acceptance is even present, or don't realize that acceptance is possible.
What is acceptance? It’s when whatever is happening right now is not being struggled with. Maybe it’s not pleasant, maybe it’s something you want to change in the future (if it’s something that can change in the future). But acceptance is noticing that it’s here, now, and not struggling with that.
Why does this matter? It’s the principle of the two arrows (this is a Buddhist thing). One arrow hits you—that’s the bad thing that’s happening. Ow. And then you struggle with it. You try to deny that you’ve been hit with the arrow, or you wish the arrow weren’t there when at least for now, you’re stuck with it (pardon the pun). You try to ignore the arrow. And all of these responses become a second arrow, which stabs you over and over again, and often hurts worse than the first.
It may be hard to conceive of this, but there is an aspect to actual pain that is the second arrow, not the first. Pain is, first and foremost, data, which you are programmed by natural selection to treat as a huge emergency. When it’s not something you can do about, you still struggle with it. This is why you can distract yourself from pain: the experience of pain as pain is partly that struggle, and by distracting yourself, you let go of the struggle until you’re done with the distraction.
As a practice, acceptance in mindfulness is reminding yourself, when something occurs, "this is happening." But that's not acceptance. Acceptance might happen as a result of this practice, or might not—e.g., true acceptance of some strong pain might not be easy to do, and even when you do it it might not be consistent—the pain stays, and the acceptance might not.
It's still a worthwhile practice to do: when you have some consistent phenomenon arising that isn't easy to accept, just sit there noticing that it is there and looking for your resistance to its being there. Don't try to make the resistance go away, or even necessarily identify it—just maintain the curious state of mind: "am I resisting this? where is the resistance?" and see what happens.