How do I make a party on the mobile version?

Start the instance of ancient ruins. Tap on "Create Chamber" and the bottom left there will be an invite button. For Ramoness Arena tap "Create Team" and there will be invite buttons on the left and right of your character.

If you mean a regular party like any other MMO, then you can't. You can join the same guild, or forge a Blood Kin pact where you get bonuses for being in the same area, but the only parties in BDM are for the Ruins or Ramoness Arena. Hope that helps!