The major advantage from having the existing business sold to you - assuming that you have a suitably-drafted purchase and sale agreement - is that there will be no question about your right to use the name of the business.
This information does not constitute legal advice and does not establish an attorney-client relationship.
You can keep it very, very simple but keep it in writing, in plain English.
In exchange for $ you buy the dba and he assures you in writing there are no surprise debts or tax liens or lawsuits etc. If there is an inventory, unless he can prove it paid, you really should do a bulk transfer notice.
It's hard for a lawyer not to think about all the other thinks to be considered in the sales of assets/shares.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
In addition to putting the agreement to purchase the business in writing, as the two above have rightly mentioned, you may also need to update some paperwork. You'll need to be sure that the County Recorder/Assessor has the new correct information for the Fictitious Business Name. Additionally, depending on the city or cities you'll be doing business in, you may need to file or update business licences or tax certificates.
ATTORNEY ADVERTISEMENT. Of course, without having heard the whole story and reviewed the relevant documents, I can't give you advice, just my general opinion. If you're serious, you should contact a local attorney, rather than relying on any opining on the Internet. Jason L. Eliaser is licensed to practice law in California (State Bar number 248394.) This is a communication concerning my availability for professional employment within the meaning of California Rule of Professional Conduct 1-400(A). Viewing of this post does not constitute the provision of legal advice and no attorney-client relationship is formed by viewing or responding to this post.
Unlike other business types, a sole proprietorship does not constitute a business entity separate and apart from the owner of the business (compare for example to a Corporation which is a separate business entitiy from a legal standpoint). Counsel have all given good advice but look at this as whether your friend who does have assets ( the name, any good will for the business, equipment, a lease if any, etc.) will transfer them to you and what you are both willing to agree upon. Not knowing the nature of the business, unless you do assume any outstanding liability (does someone out there have a potential claim?) he would be liability of any prior work or contracts.
I hope this is of some help and wish you good luck.