More casual:
* Get tangled
* Get all messed up
* Make a mess of
* Knot up
* Get into a knot
More technical:
* Entangle
* Intertwine
* Bind
* Interlace
* Snag
More descriptive:
* Form a Gordian knot (referencing the famous knot that was said to be impossible to untie)
* Become a tangled web
* Become a tangled mess
The best choice will depend on the specific situation and the tone you want to convey.