Gerund (verb + ing) or Infinitive (to + verb)

Infinitive (to + verb): 
It is often used when actions are unreal, abstract, or future.

We use infinitive after certain verbs and their object.

Examples:

• He asked me to go there with him.
• She told me to help her. 
• The police ordered the man to stop.

Verbs:
advise, allow, *ask, authorize, cause, challenge, convince, encourage,
 *expect, force, get, help, hire, inform, instruct, invite, *need, order,
 permit, persuade, *prepare, *promise, remind, require, teach, tell, train,
 urge, *want, *warn, *would like

*Some words can be used without an object as well as with an object.
 Example: I want him to go. I want to go.

We use infinitive after verbs that refer to a future event.

Verbs:
want, hope, aim, intend, arrange, attempt, promise, be, determined, plan,
consent, decide, demand, deserve, determine, endeavor, expect, mean (intention), offer, proceed, promise, threaten, swear, volunteer, want, would like, would hate, would love

We use infinitive after some adjectives. Many of these adjectives describe a person’s emotions or mental state.

Adjectives:
glad, happy, pleased, delighted, content, relieved, lucky, fortunate, sorry, sad, upset, disappointed, proud, ashamed, ready, prepared, anxious, eager, willing, motivated, determined, careful, hesitant, reluctant, afraid, surprised, amazed, astonished, shocked, stunned.

We use infinitive after "too" and "enough".

Examples:

• It's too difficult to convince him to be helpful. 
• But it's easy enough to fool him to get what you want.

We use infinitive if it can be the subject of a sentence.

Examples:

• It takes many years to save for college. 
• It is important to have good health.

We use the bare infinitive (the infinitive without 'to') after some verbs:

• modal verbs;
• let;
• make;
• (sometimes) help;
• verbs of perception (see, watch, hear, notice, feel, sense);
• expressions with 'why'.

Examples:

• I can meet you at six o'clock.
• The teacher let us leave early.
• I watched her walk away.
• why go out the night before an exam.

Gerund (verb + ing):
It is often used when actions are real, concrete, or completed

We use the gerund after verbs that express likes/dislikes.

Verbs:
like, love, enjoy, dislike, hate, mind, don't fancy,
don't mind, can't stand, can't bear

We use the gerund for an action that happens at the same time of the action of the main verb.

Examples:

• I enjoy playing

We use the gerund for an action that happens before of the action of the main verb.

Examples:

• She admitted breaking the window. [ She admitted that she had broken the window. ]
• I miss living in England. 
• I remember buying him a present.
• Mary forget meeting Tim in Italy.

We use the gerund after prepositions.

Example:

• I am interested in collecting stamps.
• After playing football I drank an orange juice.

We use the gerund with possessive forms.

Examples:

• I enjoyed their singing. 
• We discussed the machine's being broken.

We use the gerund as subject, complement, or object of a sentence.

Examples:

• Reading helps you learn English. 
• Her favorite hobby is reading. 
• I enjoy reading.