Prospects vary widely based on location, the kind of museum job you want, and education. It can be a tough job market to get into, and I caution you against jumping in (especially to a costly degree) without doing some work or volunteering in a museum first. I got my Masters degree in 2010 in Museum Studies, and the job market in the Bay Area CA is still very competitive. Try looking at entry level jobs in Museums: for instance customer service, ticketing and interpretation are all wonderful ways to get your for in the door at your local museum. Once they know you, those jobs can feed into jobs in other departments. You can then make an informed decision if this is the career for you, and whether or not pursuing an advanced degree is worthwhile to you.
Paula recommends the following next steps:
Part of getting a job in the museum field is being willing to network and start at the bottom. Many museums and heritage sites look in house first when hiring. Starting with an entry level or volunteering is a great way to get your foot in the door.
Alice recommends the following next steps: