I have some domains that might infringe on a copyright or trademarked material. MIGHT I say! So how can I set up a company or DBA so that my personal assets cannot be touched if I ever get sued or have to go to court?
Consult an attorney in your location that deals with asset protection. There are many online companies that can form a corporation or llc, but if you have substantial assets you want to protect, it really needs to be set up and run correctly. A regular company would be treated as a sole proprietorship and not offer any protection. Protection also varies by state, and you cannot shield yourself from acts of fraud. You also need to be aware that in addition the cost of the corp or llc, there will be more record keeping, costs for separation of funds, and you will likely have additional accounting/tax preparation costs.
There are many misconceptions concerning the concept of limited liability. The premise of limited liability relates only to the investor’s financial responsibility for the debts of the entity. In a limited liability entity, like a Corporation or LLC, once the shareholder has made their investment they have no further obligation with respect to the entity’s debts. However, a shareholder, particularly a shareholder who is active in the business operations, is still liable for the criminal and tortuous (i.e. negligence, fraud, sexual harassment, etc.) acts they might commit in connection with the business. Limited liability entities generally do not shield you from law suits based on issues other than debt.
Read How Limited is Limited Liability? for a more extensive discussion of some of the issues mentioned by mjewel and attorney jaffe above. Specifically, if you infringe on someone's copyright, your entity may not protect you. Having an entity own the domains may stop the copyright owner from digging further but there is no guarantee. Certainly it is easier for the copyright owner to prove that you were the one infringing when the domain is in your own name, but a persistent plaintiff can eventually discover your personal responsibility if it exists.
I would recommend you try out LegalZoom You can fill out everything online, and everything is pretty straight forward it only costs a ~$200 or more depending on what state you live in, if you do live in the US.