-ing form or to + infinitive?

The second verb depends on the first one. You have to learn the most frequent ones:

Always -ing after a preposition: interested in learning, good at cooking, before leaving, without saying, I look forward to seeing you (here “to” is a preposition). The -ing form is also the subject of a sentence: Swimming is good for you.

Change of meaning:

• stop doing (no longer do) / stop to do (stop in order to do): I stopped smoking. I stopped to smoke.
• remember / forget doing (a past memory) / to do (a task): I remember meeting him. Remember to lock the door.
• try doing (experiment) / try to do (make an effort): Try restarting the computer. I tried to open it, but I couldn't.

Like, love, hate, prefer, start, begin, continue: both forms, same meaning: It started raining / to rain.

Base verb without to after modals and after make and let: She made me laugh. Let me help. With want + person: I want you to come (not “I want that you come”).