Das Maedchen moechte im Baum klettern. Sie mag den Baum. Sie darf im Baum klettern, aber sie muss aufpassen. Sonst kann sie leicht runterfallen.
Modal verbs, also called modal auxiliaries, show us how the speaker views what he or she is saying. The main verb shows the action. The modal verb gives us the information about the manner of doing something.
- I can play various instruments. (shows the ability to play)
- Ich kann verschiedene Instrumente spielen. (Infinitive: koennen)
- I should spend more time practising. (ought to practise more)
- Ich sollte mehr ueben. (Infinitive: sollen)
- I must find more time to do so. (have to find more time)
- Ich muss mehr Zeit dafuer finden. (Infinitive: muessen)
German has also a group of modal verbs, die Modalverben. They  usually make no sense when alone in a clause and occur with a main verb. The modal verb is the one which needs to be conjugated, like in English it is directly linked with the subject.
Ich kann. ( I can.) This is an incomplete sentence and makes no sense.
Ich kann ein Instrument spielen. ( I can play an instrument.) This is the full sentence. Please note; the modal verb is conjugated, the main verb in it's infinite form.
When asking questions with a modal verb the response usually doesn't require repeating the main verb.
Kannst du ein Instrument spielen? ( Can you play an instrument?)
Ich kann. (I can.)
Here are some examples how to use modal verbs in German language:
moechten: is used to express a wish, the more polite form of wollen
- Ich moechte gern einen Kaffee trinken und die Zeitung lesen. (I would like to drink a coffee and read the paper.)
- Moechtest du morgen ins Kino gehen? (Would you like to go to the movies tomorrow?)
wollen: is also used to express a wish, the stronger form of moechten
- Sie will an der Universitaet studieren. (She wants to study at University.)
- Wollt ihr morgen ins Kino gehen? (Do you want to go to the movies tomorrow?)
duerfen: is used to express that something is allowed, or in the negative form that something is forbidden
- Hier darf man rauchen. (Smoking is allowed.)
- Hier darf man nicht rauchen. (Smoking is not allowed/ prohibited.)
muessen: is used to express a necessity or obligation
- Er muss viel fuer die Pruefung lernen.  (He has to study a lot for the exam.)
- Muessen wir wirklich schon gehen? (Do we really have to go already.)
koennen: is used:
1. to express that someone/ something is able to do something
- Das Kind kann schon mit 10 Monaten laufen.  (The 10 month old child can already walk.)
- Kannst du bitte den Abwasch machen?  (Can you do the dishes?)
2. to express that something is permitted
- Koennen wir heute abend lange fernsehen?   (Can we watch telly late until late tonight?)
3. to express that something is possible
- In Deutschland kann man in vielen Restaurants rauchen.  (Smoking is permitted in a lot of restaurants in Germany.)
sollen: is used to express that something is supposed to be done, should be done
- Das Kind soll naechstes Jahr in die Schule gehen.  (The  child is supposed to start school next year.)
- Du sollst nicht immer so laut sein?  (You shoudn't be that noisy all the time.)
And this is how to conjugate German modal verbs:
Infinitive
ich
du
er / sie / es
wir
ihr
sie
English
duerfen
darf
darfst
darf
duerfen
duerft
duerfen
may / to be allowed to
koennen
kann
kannst
kann
koennen
koennt
koennen
can /to be able to
moegen
mag
magst
mag
moegen
moegt
moegen
to like
muessen
muss
musst
muss
muessen
muesst
muessen
must / to have to
sollen
soll
sollst
soll
sollen
sollt
sollen
should /to be supposed to/ ought to
wollen
will
willst
will
wollen
wollt
wollen
to want
