1. Modal Verbs In German there are 6 modal verbs:
Their function is to modify the meaning of other verbs.
German
English
können
To be able to, to know how to, can
müssen
To have to, must (necessity)
wollen
To want to
dürfen
To be allowed/permitted to
sollen
To be supposed to, is to (strong order)
mögen
To like

2. Modal Verbs Subject Predicate Verb Other Parts of Speech
You recall that word order in statements is as follows:
Nina and Alexander go/are going to the disco.
When a modal verb is added, the sentence would appear as follows.
The sentence now reads: Nina and Alexander want to go to the disco.
Notice now that the modal verb is in the 2nd position (Verb1), while the infinitive verb (modified by the modal verb) is placed at the end of the clause/sentence (Verb2).
Subject
Predicate
Verb Other Parts of Speech
Nina und Alexander
gehen in die Disco
Subject
Predicate
Verb Other Parts of Speech Verb2
Nina und Alexander
wollen in die Disco gehen

3. Modal Verbs Additional Examples
German
English
Ich kann gut kochen.
I can cook well.
Ihr müsst um Uhr zu Hause sein.
You have to be home at 5 p.m.
Willst du ins Kino gehen?
Do you want to go to the movies?
Darf ich den Film sehen, Mutti?
May I see the movie, mom?
Sie soll ihre Hausaufgaben machen.
She should do her homework.
Mögen Sie auch Wein, Frau Ziegler?
Do you also like wine, Mrs. Ziegler?
Questions with modal verbs follow similar rules as questions without modal verbs. The modal verb is placed 1st, followed by the subject in the 2nd position.
Notice the placement of Mutti. When directing a question to someone, the infinitive is placed at the end of the clause, followed by a comma and the person whom you are speaking to.

4. Modal Verbs Möchte versus Mögen
The modal verb möchte is a derivative of the modal verb mögen and means would like versus like or want. It is often used to ask politely for something.
See the difference between these three sentences.
Ich mag Schnitzel. (I like Schnitzel)
Ich will Schnitzel essen. (I want to eat Schnitzel).
Ich möchte Schnitzel essen. (I would like to eat Schnitzel)
NOTE: when describing the liking of an activity, it is more common to use the adverb gern versus using mögen which expresses “absolute” likes/dislikes. Therefore ich esse gern Schnitzel would be the appropriate way of expressing you like to eat Schnitzel versus ich mag Schnitzel essen.

5. Modal Verbs Position of nicht
Ich kann heute Morgen kommen.
Ich kann nicht heute Morgen kommen, sondern heute Nachmittag.
Notice the position of nicht is placed before the part of speech that is negated. By doing so, you are emphasizing you cannot come this morning. If you simply could not come, the sentence would appear as follows:
Ich kann heute Morgen nicht kommen.

6. Modal Verbs Omission of Infinitive
Sometimes it is not necessary to add the infinitive verb if the meaning of the sentence containing a modal is clear.
For example:
Ich muss nach Hause
It is implied that you have to go home (to go, drive, run) in this sentence. Since this distinction is clear, the modal may be omitted.
Ich möchte einen Kaffee
It is implied you would like a coffee (to drink, have, order, etc.) but it is not necessary to include either of those infinitive verbs.
gehen / fahren / laufen.
trinken / haben / bestellen.

7. deine Hausafgaben machen
gut kochen
deine Hausafgaben machen
ins Kino gehen?

8. gut schwimmen
zum Arzt gehen
das Fenster aufmachen?