An infinitive clause is dependent on the main clause of the sentence for its meaning.

It has no grammatical subject, only an implied one, and therefore no conjugated verb.

Verbs in a main clause that often introduce an infinitive clause:

to plan/intend/decide/hope to do something

to forget to do something

to try/promise/suggest to do something

 

it is nice/hard/difficult/complicated etc. to do something

The infinitive, preceded by the word "zu", goes to the end of the infinitive clause, e.g.

Sie plant, nach Deutschland zu fahren. (She plans to travel to Germany.)

Ich hoffe, meinen Freund auf der Party zu treffen. (I hope to meet my friend at the party.)

Er vergisst immer, seine  Hausaufgaben zu machen. (He always forgets to do his homework.)

If the verb in question has a separable prefix, the "zu" goes between the prefix and the stem of the infinitive, e.g.

aufstehen, er steht auf: Sie plant, morgen früher aufzustehen. (She plans to get up earlier tomorrow.)

ankommen, er kommt an: Ich hoffe, bald in Berlin anzukommen. (I hope to arrive soon in Berlin.)

mitnehmen, er nimmt mit: Er vergisst immer, seinen Regenschirm mitzunehmen. (He always forgets to bring his umbrella.)

An infinitive clause that contains only the verb and possibly an adverb is not set off by a comma, while those with other elements usually are, e.g.

Ich plane zu bleiben. (I plan to stay.)

Ich plane, drei Tage in Frankfurt zu bleiben. (I plan to stay three days in Frankfurt.)