You know hoffen and you know sehen. Then a message arrives:
Ich hoffe, dich bald zu sehen. — I hope to see you soon.
The comma promises a second clause, and a second clause needs a subject and a conjugated verb. This one has neither.
The clause with no subject of its own
This is an infinitive clause: zu plus an infinitive at the very end, everything else stacked in front. It has no subject and no conjugated verb, because it borrows its actor from the main clause.
The difference from a dass-clause:
Ich hoffe, dass ich dich bald sehe.
Ich hoffe, dich bald zu sehen.
Same meaning. The first names ich twice and conjugates sehen; the second names it once and lets the infinitive stand. After verbs like hoffen and versuchen, German reaches for the second, the way English says I hope to see you rather than I hope that I will see you. After others the dass-clause stays the everyday form and the infinitive sounds stiff — Ich glaube, dass ich ihn kenne, not Ich glaube, ihn zu kennen.
The borrowed actor is usually the main subject, but it does not have to be. After bitten, empfehlen, raten, erlauben and verbieten it is the object instead — accusative after bitten, dative after the other four:
Ich bitte dich, mir zu helfen. — I'm asking you to help me. (you help, not I)
Ich empfehle dir, früher zu kommen. — I'd advise you to come earlier.
If the actor is named nowhere in the main clause, you need dass — see German subordinate clauses:
Ich hoffe, dass du bald kommst. — I hope you come soon.
Where zu goes when the verb is separable
If the infinitive is separable, zu does not stand in front of it — it goes inside, between prefix and stem, as one word:
Ich habe vergessen, dich anzurufen. — I forgot to call you.
It is the slot the ge- takes in the perfect — angerufen, eingekauft — familiar from separable verbs. Inseparable verbs keep zu outside: zu verstehen, zu bezahlen.
The verbs that take a zu-clause
Most of them — the default, which is why there is no list worth memorising. hoffen, versuchen, vergessen, anfangen, sich freuen: all one shape, Ich versuche, pünktlich zu sein. Nouns and adjectives open one too — Ich habe keine Zeit, das zu machen.
brauchen comes with a condition attached. It takes a zu-clause only under a negation or a limiter — nicht, kein, nie, nur, kaum:
Du brauchst nicht zu kommen. — You don't have to come.
Du brauchst nur anzurufen. — You only need to call.
Without one of those the sentence needs müssen: Du musst kommen. Du brauchst zu kommen is not German.
The verbs that take no zu at all
A short group, worth learning as a list — nothing about a verb predicts membership. After these the bare infinitive goes to the end with nothing in front:
- the modal verbs — können, müssen, wollen, sollen, dürfen, mögen (see German modal verbs)
- werden — which is why the future is Ich werde kommen, never zu kommen
- perception: sehen, hören, fühlen
- lassen — having something done, letting something happen
- movement and sending: gehen, kommen, fahren, schicken, and bleiben with them
Ich lasse mein Auto reparieren. — I'm having my car repaired.
Er kommt uns besuchen. — He's coming to visit us.
helfen goes either way: short complement, no zu; longer clause, zu.
Er hilft mir aufräumen.
Er hilft mir, die Küche aufzuräumen.
lehren and lernen do the same.
um ... zu, and the moment you need damit
um ... zu is the same clause with purpose attached: in order to. It answers wozu?
Ich lerne Deutsch, um in Wien zu studieren. — I'm learning German in order to study in Vienna.
The um-clause has no subject of its own, so its actor has to be recoverable from the main clause — normally the main subject, though in the two fixed cases below it is a general man. Name a different actor and you need damit: an ordinary subordinate clause, own subject, verb at the end.
Ich spare Geld, um ein Auto zu kaufen. — (I save, I buy)
Ich spare Geld, damit meine Tochter studieren kann. — (I save, she studies)
After a verb of motion the purpose um can be dropped: Er kam(, um) mich zu besuchen. Two places where it cannot be: after genug, and after intensifying zu plus an adjective — zu in its "too" sense, not the zu this guide is about.
Sie ist alt genug, um allein zu reisen. — She is old enough to travel alone.
Der Koffer ist zu schwer, um ihn zu tragen. — The suitcase is too heavy to carry.
In both, the recovered actor is a general man — the suitcase is not the one carrying.
ohne ... zu and statt ... zu
Same construction, same actor test.
Er ist gegangen, ohne sich zu verabschieden. — He left without saying goodbye.
Statt zu arbeiten, hat er den ganzen Tag ferngesehen. — Instead of working, he watched TV all day.
statt and anstatt are interchangeable here. A different actor turns both into ohne dass and (an)statt dass:
Er ist gegangen, ohne dass ich es gemerkt habe. — He left without my noticing.
The comma, honestly
The comma is required in the cases you use most: with um, ohne and (an)statt, when the clause hangs off a noun (keine Zeit, das zu machen), and when a da- word announces it (Ich freue mich darauf, dich zu sehen — see da- and wo- compounds).
Outside those, the current rules (1996, revised 2006) make it optional: Ich versuche(,) pünktlich zu kommen is correct either way.
A bare zu + infinitive, with nothing else inside it, takes no comma — Es fängt an zu regnen, Er scheint zu schlafen. Same where the infinitive is welded to the main verb: Ich habe noch viel zu tun.
What to actually memorise
Where zu lands in a separable verb — anzurufen, never an zu rufen or zu anrufen. Purely mechanical, and the most often botched.
The no-zu group: the six modals plus werden, sehen, hören, fühlen, lassen, gehen, kommen, fahren, bleiben and schicken, with helfen, lehren and lernen going either way. Anything else that takes an infinitive complement takes zu.
The actor has to be findable in the main clause — normally the subject, or the object after bitten, empfehlen, raten, erlauben and verbieten. After genug and intensifying zu it is a general man. Named nowhere at all, you switch to dass. A different actor after um, ohne or statt switches you to damit, ohne dass and (an)statt dass.
A zu-clause after brauchen needs a negation or a limiter — otherwise the verb you want is müssen.