fliegen
to fly
To move through the air using wings or an engine.
Nächstes Jahr fliegen wir für drei Wochen nach Kanada.
Next year we're flying to Canada for three weeks.

to fly
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to fly
To move through the air using wings or an engine.
Nächstes Jahr fliegen wir für drei Wochen nach Kanada.
Next year we're flying to Canada for three weeks.

'Fliegen' (to fly) is a verb of movement and always forms the perfect tense with the auxiliary verb 'sein' (to be). So the form is 'ich bin geflogen' (I flew / I have flown), not 'ich habe geflogen'.
Wir sind letzten Sommer nach Spanien geflogen.
We flew to Spain last summer.
'Fliegen' (to fly) is a strong verb. Pay attention to the vowel change: in the simple past it becomes 'flog', and in the past participle it becomes 'geflogen'.
Als Kind flog ich zum ersten Mal mit einem Flugzeug.
As a child, I flew in an airplane for the first time.
To specify a travel destination, use 'nach' for most cities and countries without an article. For countries with an article (e.g. 'die Schweiz' (Switzerland), 'die USA' (the USA)), use 'in' with the accusative.
Nächstes Jahr fliege ich nach Japan.
Next year I'm flying to Japan.
The meaning 'entlassen werden' (to be dismissed / fired) is colloquial. The prepositions 'von' or 'aus' are often used with it: 'von der Schule fliegen' (to get kicked out of school) or 'aus dem Kurs fliegen' (to get kicked out of the course).
Wenn du noch einmal zu spät kommst, fliegst du aus dem Team.
If you're late one more time, you'll get kicked off the team.
The expression 'die Zeit fliegt' (time flies) or 'die Zeit vergeht wie im Flug' (time flies by) is very common. It expresses that time seems to pass very quickly.
Wenn man Spaß hat, vergeht die Zeit wie im Flug.
When you're having fun, time flies by.
The colloquial expression 'auf jemanden/etwas fliegen' (to be crazy about someone/something) is always formed with the preposition 'auf' and the accusative. It means that you really like someone or something.
Mein Bruder fliegt total auf Science-Fiction-Filme.
My brother is totally crazy about science fiction films.
to drive / ride
'fahren' and 'fliegen' both describe movement or travel. The difference is mainly in the means of transport and the route. 'fahren' is used with cars, buses, trains, bicycles, or other vehicles on the ground. It can also mean that you are driving or operating a vehicle yourself. 'fliegen' is used when something moves through the air, especially when traveling by plane. Learners sometimes confuse the words because both are used for travel. As a practical rule: you use 'fahren' with a train, car, or bus; you use 'fliegen' with a plane.

Im Sommer fliegen wir mit den Kindern nach Spanien.
In the summer, we are flying to Spain with the children.
Vor dem Termin fährt die Lehrerin mit dem Bus ins Krankenhaus.
Before the appointment, the teacher takes the bus to the hospital.