nähen
to sew
To join or work with fabric, leather, or other materials using a needle and thread in order to make or repair clothing or other objects.
Sie hat gelernt, ihre eigenen Kleider zu nähen.
She learned to sew her own dresses.

to sew / stitch
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to sew
To join or work with fabric, leather, or other materials using a needle and thread in order to make or repair clothing or other objects.
Sie hat gelernt, ihre eigenen Kleider zu nähen.
She learned to sew her own dresses.

The verb 'nähen' (to sew / stitch) is the base for other useful words. 'Die Naht' (the seam) is the line where two pieces of fabric are joined, and 'die Nähmaschine' (the sewing machine) is the device used for sewing.
An meiner Jacke ist eine Naht aufgegangen.
A seam has come undone on my jacket.
The object of the verb makes clear which meaning is intended. If you sew 'ein Kleid' (a dress), 'einen Vorhang' (a curtain), or 'einen Knopf' (a button), the craft activity is meant. If you stitch 'eine Wunde' (a wound), the medical procedure is meant.
Der Arzt erklärte, dass er die Wunde sofort nähen müsse.
The doctor explained that he had to stitch the wound immediately.
Different prepositions describe the sewing action more precisely. You sew something 'an' something (a button onto a shirt), 'auf' something (a patch onto a pair of trousers), or 'aus' something (a dress out of linen).
Kannst du mir diesen Knopf wieder an meine Jacke nähen?
Can you sew this button back onto my jacket for me?
In a medical context, 'nähen' (to stitch) is very often used in the passive, because the person with the wound does not perform the action themselves. A typical formulation is: 'Die Wunde musste genäht werden.' (The wound had to be stitched.)
Nach dem kleinen Unfall musste sein Kinn mit drei Stichen genäht werden.
After the small accident, his chin had to be stitched with three stitches.
to connect / to bandage
'verbinden' and 'nähen' can both have to do with holding material or a wound together. 'verbinden' is more general: you can connect things technically or physically, and you can protect a wound with a bandage. 'nähen' is more specific and means working with a needle and thread, for example with fabric or, in medicine, with a wound. The risk of confusion is especially high with wounds: 'eine Wunde verbinden' means to put a bandage around a wound; 'eine Wunde nähen' means to close it with medical thread.

Der Arzt muss die tiefe Wunde am Arm nähen.
The doctor has to stitch the deep wound on the arm.
Nach dem Sturz verbindet die Ärztin die Wunde am Knie.
After the fall, the doctor bandages the wound on the knee.