You either draft a written offer yourself or you have a licensed real estate agent (preferably a Realtor) draft one for you and submit it to the seller or their agent for consideration. A verbal offer and acceptance is meaningless in real estate unless it is for a short term rental.
Writing your own contracts is perfectly possible, and legal. But it's also an incredibly bad idea. There's two reasons for this: Property law is complicated. Because it's such a fundamental part of legislation, it's often lots and lots of different laws layered on top of each other.