Zu with Infinitives

Infinitives are usually preceded by zu except when modals are used.  If a separable prefix is used in the infinitive, the zu is inserted between the prefix and the stem.

Hast du Lust, den Dom zu besichtigen?  Do you feel like visiting the cathedral?
Es dauert lange, durch die Stadt zu fahren.  It takes a long time to drive through the city.
Es ist zu früh, sich aufzustehen.  It is too early to get up.

Um, ohne and anstatt can be used with zu as well.  They introduce infinitival clauses.  Um.. zu is used to indicate purpose, while ohne...zu and anstatt...zu are used with infinitives, and translated as present participles in English.  (Um...zu must be used instead of just zu when the English equivalent "in order to" can be used sensibly.)

Er kam, um das Buch abzuholen.  He came in order to pick up the book.
Sie sagte es, ohne mich anzusehen.  She said it, without looking at me.
Statt hier zu sitzen, sollten wir ihn suchen.  Instead of sitting here, we should look for him.

Sein + zu + an infinitive are used the same way in English and German, but the construction is far more common in German.

Das ist nicht zu machen.  That can't be done.
Das ist in jedem Laden zu finden.  That can be found in any store.

Expressions of Time

The accusative case is used to indicate definite time when no preposition is used.

Letzten Sonntag blieb ich zu Hause.  Last Sunday I stayed home.
Sie fährt nächste Woche nach Deutschland.  She's going to Germany next week.
Er hats uns voriges Jahr besucht.  He visited us last year.

Time expressions with the prepositions an, in and vor are in the dative case.

Wir müssen am Sonntag zurück.  We must return on Sunday.
In der Nacht wird es kalt.  It gets cold at night.
Vor drei Jahren war es hier genau so kalt.  Three years ago it was just as cold here.

The genitive case is used to express indefinite time, and may refer to the future or past.

Eines Tages war er krank.  One day he was sick.
Eines Morgens kommet er zu spät.  One morning he'll be late.