Fügen is a verb that means "to join," "to fit," or "to add." In its reflexive form, sich fügen, it means "to comply" or "to submit." You will often see it with a prefix, and that is what we want to talk about today. Here are three particularly common verbs: 

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Es gibt drei weitere Wörter, die du einfügen kannst.

There are three more words that you can insert.

Caption 52, Deutsch mit Eylin: Höflich sprechen, Konjunktiv 2 benutzen

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Als Nächstes können wir die Nudeln und den Blumenkohl hinzufügen.

Next, we can add the pasta and the cauliflower.

Caption 29, Bundesländer und ihre Rezepte: Niedersachsen

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Zudem verfügen sie über einen ausgezeichneten Geruchssinn.

They also have an excellent sense of smell.

Caption 55, Evolution: Meeresbewohner

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There is also the related expression zur Verfügung stehen ("to be available"). The noun die Geringfügigkeit, on the other hand, refers to insignificance.

Der Computer steht Ihnen zur Verfügung.

The computer is available to you.

Caption 24, Berufsleben: das Vorstellungsgespräch

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Und wenn es nur um fiese E-Mails geht, dann wird es bei Gericht wegen Geringfügigkeit abgelehnt.

And if it's only about nasty emails, then it will be rejected in court because of insignificance.

Captions 20-21, Die Pfefferkörner: Gerüchteküche

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The verb (sich) fügen should not be confused with fugen, which is more of a technical verb used in construction and craftsmanship. It most often refers to creating or filling joints between tiles, bricks, or other building materials. It is rarely used with a prefix or in its reflexive form. If you can remember that die Fuge (without an umlaut) means "the gap" or "the joint," this can perhaps help you to not get the verbs mixed up. 

Die Fliesen müssen noch gefugt werden.
The tiles still need to be grouted.

Der Tischler fugte die Holzbretter perfekt ineinander. 
The carpenter joined the wooden boards perfectly.

Interestingly, the other meaning of die Fuge is a type of musical composition featuring a main melody that is imitated and joined by additional melodies that are woven together. As you may have guessed, this is known as a "fugue" in English.

Further Learning
You will find many more versions of the words above used in context on Yabla German.