You need a contract. I've been doing business since 1994 under what some folk refer to as a freelancer (I call it contracting consultant). Without agreed project deliveables, you will carry the risk of a customer who is never happy, constant changes being asked from you and your expectations of your costs being covered, and your customers interpretation of you correcting without cost what they perceive to mistakes.
In addition, depending on what country you are in, without a contract and without clear deliverables, you could be considered an employee. Europe (especially the UK) would see it this way. It leaves the employer open to taxes, paying you sick pay, pension, other benefits (if other employees get car, paid cell phone or health insurance, then you would also qualify).
When in business, the agreement is never between two people (buyer of services and provider of services). There is also laws, and tax laws. Regardless of you or your employers general understanding, the law of the land applies.
So even if you don't care about the taxman - think about your relationship with the customer. Break your project down to the most basic goal, agree on that, then once you deliver that, agree the next step... Do that and you two will have a long lasting happy relationship.
A previous Q&A that I did should interest you - even if you are from a different country, you should at least read and consider the points https://startups.stackexchange.com/questions/8576/how-to-build-a-startup-freelance-software-qa-in-the-us/8585#8585
Best of luck!