Before moving on, you've got to move out
Whether leaving a marriage or a non-legally binding cohabitation, one thing is immediately inevitable: at least one person will certainly be physically moving out. And the sooner is probably the better.
The price of a move varies on how much stuff you have and how far you're going. The average professional moving service will cost several hundred dollars for a simple in-town move (moving across zip codes can up the costs dramatically). The cheaper option is to rent a U-Haul, which offers local rentals for around $20/day plus the cost of a pizza and some beer to persuade some friends to help out with the heavy lifting. And of course, you can always hit-up Craigslist to hire the ubiquitous "man with a van," who come in a wide range of price tags and levels of legitimacy.
As you search out a new place to live—especially if you are in a hurry—you may find it necessary to place some of your stuff in storage. These prices vary widely depending on your needs. Bundle.com's database of aggregated and anonymized credit card data shows that the average total price spent at storage facilities in most parts of the country is between $100 and $300.
Keep in mind, that you may need to wait a month until you can move into a rental space. If things are really heated at home, and you don't have any friends or family to couch surf with until your new home is available, you may have to stay at a hotel, or even a hostel. This is obviously a more expensive and annoying path. If you're not able to share the same bed, hopefully you can still share the same place, at least for a little while.