We recently had the question: If I encounter a verb in the Duden, how can I tell which grammatical cases and prepositions to use with that verb?
Although that question only talks about cases (i.e. nouns or nominals) and prepositions, one could just as well add verbs to it and the answer would remain the same: It simply has to be learned (i) whether a verb can be combined with another verb and (ii) what form the dependent verb takes.
German has three infinitives governed by verbs (Statusrektion):
- einfacher Infinitiv, bare infinitive: gehen
- zu-Infinitiv, infinitive with zu: zu gehen
- Partizip II, past participle: gegangen
Learners will encounter these bit by bit when they are taught periphrastic tenses, moods, and voices. To give an example for each:
- bare infinitive with modal verbs:
ich/er/sie will, muss, kann … gehen
- infinitive with zu with scheinen and the modal passive:
die Strategie scheint zu funktionieren, die Regeln sind einzuhalten
- past participle in the perfect and passive:
sie hat gewartet, er ist gegangen; die Kinder werden abgeholt
This is exactly the same pattern as with non-verbal objects, where the following contrasts have to be learned as well:
Ich helfe dir. Ich unterstütze dich.
Er fürchtet mich. Er fürchtet sich vor mir.
While the most important verbs governing infinitives, i.e. those used in expressing periphrastic tenses, moods, voices, are introduced in textbooks, learners will have to learn the rest by looking at examples in dictionaries. Let me give one example for each type of infinitive.
For machen, DWDS has under 7a:
jmdn. stutzen, frösteln, lachen, weinen, etw. vergessen machen
For brauchen, under 1b:
etw. nicht zu tun brauchen (= etw. nicht tun müssen)
For kommen, under 1e:
gelaufen, gefahren, geritten kommen
One important final point: Of the three infinitives mentioned above, infinitive with zu are special in that they and only they can appear in subordinate clauses (Infinitivkonstruktionen). Therefore, googling Verben mit zu-Infinitiv will get you lists of verbs that have clauses as complements, such as versprechen and versuchen. The examples above are different in that two verbs combine within a single clause.