Your question is a very big one. At this point I assume that the other party is amenable to such an offer?
Buying into a business is a very big deal just like getting married. What do you know about the partners (backgrounds, litigation)? What do you know about the health of the business (debts, liabilities)?
You are asking about how to paper this. What is the structure (c-corp, s-corp, LLC)? Do they already have a shareholder or operating agreement drafted?: Have you reviewed it? Will they present you with a subscription agreement or stock purchase agreement?
There are plenty of examples of contracts online but you certainly cannot expect any of them to comport with your specifc needs.
I think it would be helpful if you discussed your objectives over with a lawyer in private. Most of us here, including myself, offer a free phone consult.
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There is no "off the shelf" form for your customized goal. A lawyer would probably require a few hours. I cannot believe anyone is still buying domain names, but if you have received a "large" offer, it is probably worth the investment to make sure your share of the company is validly issued and worth "something".
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.
You cannot use a sample form for a complex business transaction such as this. If you are receiving a "large amount of money" in the transaction, then surely you can afford legal counsel. You need legal counsel to protect you because if you receive equity in a company, you face many important legal issues and risks. You need to enter into agreements with the partners or shareholders of the company, but before doing so, you need to make sure you want to get involved with them. Who are these people? What is the financial condition of the company? Will you be assuming any unexpected financial risk if you get involved with this people? What procedures will be in place to govern your share of revenues or profits of this company? What happens if you want to sell your equity interest---how easily will you be able get out of the company when you want to? These and dozens of other issues need to be covered in agreements and negotiated with the parties. Obviously, you need to retain experienced legal counsel for this.
I must say, moreover, that I am surprised that anyone is willing to pay a "large amount of money" for a domain name. Increased enforcement against illegal cybersquatting has substantially diminished the extent to which people can successfully profit by registering and selling domain names which they are not actually using. In this regard, your counsel will need to protect you from subsequent claim by your new equity partners that you committed a fraud or otherwise wrongfully enriched yourself by selling this domain name to them.