-Ing or to + infinitive
When two actions appear together, you need two verbs. In this case, the second verb should be either an -ing form or an infinitive. As you have read in the section CleverCookie's notes, there is a historical reason for this, and, although practising would lead you to success, lists are quite handy in this case (thanks, Cambridge Dictionary Online).
Followed by -ing
Followed by to + infinitive
mean (= intend)
There are also some special cases you must consider.
Some verbs can be followed by - ing or a to + infinitive with no change in meaning:
I begin to work. = I begin working.
It started to rain. = It started raining.
Or little difference in meaning:
I love, hate, prefer, like cooking = emphasis on the process.
I love, hate, prefer, like to cook. = emphasis on the result.
But others do make a difference: go on, need, remember, forget, try, mean, regret, stop, and want.
She forgot to call. = She did not call because she forgot she had to do it.
She forgot calling. = She did not have a memory of calling before.
She remembered to call. = She called because she remembered she had to do it.
She remembered calling. = She had a memory of calling before.
She tried to call. = Calling was difficult, but she tried.
She tried calling. = Calling was an option among others.
She stopped to call. = She stopped an action to call.
She stopped calling. = She gave up the action of calling.
Some verbs can also be followed by an infinitive without to, with both or by either an -ing or to + infinitive:
Followed by an infinitive without to (always with an object):
She let me enter the room.
My teacher made it happen.
Followed by either:
They help me finish. -------- with an object.
They help to finish. ---------- without an object.
Followed by an infinitive without to or by -ing: feel, notice, see, hear, overhear, and watch.
To emphasise the action in progress: I saw him falling from the building.
To emphasise the whole event: I saw him fall from the building.