Use can + the base verb for something you are able to do now or in general. Use could for something you were able to do in the past. After can or could, use the base verb with no to and no -s.
can / could to say what you are able to do
I can swim.
She can speak three languages.
When I was five, I could read.
He couldn't ride a bike last year.
Not "She cans swim. / I can to swim." — say "She can swim. / I can swim.". After can, use the base verb: no -s and no to.
Try it: Maria is a great swimmer. She ___ swim very fast. (can / cans / can to) Answer: can — For something you are able to do, use can + the base verb: She can swim. There is no -s (not "cans") and no to (not "can to") after can.
Try it: Last year Tom took lessons. Before that, he ___ ride a bike at all. (couldn't / can't / doesn't) Answer: couldn't — For an ability in the past, use could / couldn't: he couldn't ride a bike. "Can't" is about now, and "doesn't" is for present habits, not past ability.
Can I ...? to ask if it's okay
You know can for things you are able to do. You also use Can I + the base verb to ask if something is okay to do.
Can I use your phone?
Can I sit here?
Can we leave early today?
Try it: ___ I sit here, or is this seat taken? (Can / Do / Am) Answer: Can — To ask if it is okay to do something, start with Can: Can I sit here? "Do I sit" asks about a habit, and "Am I sit" is not a real form.
Could I ...? a softer way
Could I + the base verb means the same as Can I, but it sounds softer and more polite. Use it with people you do not know well, or to be extra polite.
Could I borrow your pen, please?
Could I ask you a question?
Could we see the menu, please?
Try it: At the bank, Amina asks politely: "___ I speak to the manager, please?" (Could / Do / Should) Answer: Could — Could I is the soft, polite way to ask if something is okay: Could I speak to the manager? "Do I speak" asks about a habit, and "Should I" asks for advice, not permission.
Could you ...? to ask someone for help
To ask another person to do something politely, use Could you + the base verb. There is no to after it.
Could you help me, please?
Could you open the window?
Could you say that again?
Not "Could you to help me?" — say "Could you help me?". No to after could you: just the base verb.
Try it: ___ help me carry these bags, please? (Could you / Could you to / Are you) Answer: Could you — To ask someone politely, use Could you + the base verb: Could you help me? There is no to (not "Could you to help"), and "Are you" would ask what they are doing, not make a request.
Try it: You ask two polite favours: "___ I borrow your pen, please? And then ___ you check my spelling for me?" (Could … could / Could … do / Do … could) Answer: Could … could — Could works both ways: asking to do something yourself, and asking someone else to.