It depends on a lot of factors, but I would say you're looking at between $5000 and $10,000. Saigon is a popular destination for foreigners due to the low cost of living and the fact that there's always something new to see or do.
You'll want to research the different neighborhoods in the city, so that you have a good idea of what your new home will look like. You'll also want to figure out how you're going to get around: whether you'll be driving, taking public transport, or riding your bike; because all three can be viable options in Saigon depending on your destination. Make sure you have a job lined up or some source of income to live in the country long term.
If you're shipping your material belongings from your home country to Vietnam, that's going to cost a lot more. I would suggest only bringing your most valuable things like photos, laptop, phone, clothes, etc. and starting fresh.