To soundproof a door make it structurally strong enough to block noise by replacing it with a solid core door or by adding mass loaded vinyl soundproof blankets and panels to the existing door.
Soundproof door panel.
To soundproof a door install a curtain rod over the back of the door and get a heavy fabric drape to hang from the rod.
These panels offer a step up from gluing a sheet of plywood to your door but they re not generally as expensive as high end solutions like fiberglass soundproofing blankets.
Then seal the gaps with a door gasket door sweep or spray foam to prevent air leaks.
You can also coat the door with sound absorbing paint which can reduce external noise by nearly 30.
Acoustic door blanket panels overlap the door and extend beyond the frame to prevent acoustical leaks.
If you are willing to change your doorframe to a metal one then this is a very effective door sealing method which will make a huge difference to the sound resistance of your door.
Magnetic door gaskets only work on doors which are built into metal frames so they aren t a suitable method of soundproofing for most doors.
If adding many soundproofing elements to your door seems like too much work try adding an acoustic door panel.