Hi,
I have bought five houses, more cars for ourselves and four now adult children than I can recall, and three sailboats, and have used a process that has worked well for me. It's great that the owners seem nice and avoiding a broker may save you some money if the owners are a bit flexible. I am no expert in this, but the following may be helpful. Firstly, do due diligence to ensure that they actually own the boat and that there are no loans/liens/outstanding marina or repair bills against it--not likely, but be careful. Then do your own inspection of the boat (get a friend to help if you are inexperienced). Be respectful of the owner and point out positives to ensure they see you as being fair in your inspection, but also point out problems or repairs that you identify so they can see how you might formulate an offer. Try to accurately estimate the cost of repairs (make phone calls as necessary) so you can build that into the offer. Ask lots of questions about the number and type of previous owners, and maintenance that the boat has had, especially in the last few years. Try to avoid getting too emotionally attached as you go through this process, as you need to remain as objective as possible. Check for your model/year on Yachtworld website for comparison prices, especially in your geographic area, but beyond as well to get a feel for the market. Try to determine why the owner wants to sell, as that may affect his sense of urgency and flexibility.
At that point, when you have all the information you feel you need to confidently make an offer, I would sit down with the owner(s) over a coffee or in some comfortable place, describe what you have found and learned, and suggest a purchase price that you think is fair but slightly lower to leave some room for negotiation. Most boats sell for about 15% less than asking price, but sometimes much less depending on the situation. Also add in any additional clauses or factors that you want the owner to consider--such as subject to a satisfactory survey that you will arrange, a sail test to ensure the engine starts and you like the way the boat handles, any repairs you want them to complete before purchase, what items you want included (like dinghy, life jackets, anchor, bbq, etc.), date of transfer, think about where you will moor the boat (many marinas have wait lists). Then ask their thoughts on your offer and listen carefully, remain respectful, be willing to negotiate a bit depending on their reaction and reasons. But also be prepared to walk away, as there is always another boat, that may be even more suitable for you.
Once you have both agreed on the price and conditions, it's time to write it up. I don't do this in advance as it would result in too many changes, and informal discussion is more friendly until you reach agreement. Check with your local authorities as to what kind of bill of sale is required, and any special contents or process. The boat paperwork will likely need to be formally transferred at a local office. If you feel uncertain, and maybe even if you feel reasonable confident, you could have the final sale subject to satisfactory review by your lawyer, and have him or her take a look at it to be sure.
If you can arrange for the owner to spend some more time to show you all the intricacies of the boat, and maybe go for a full day sail together to learn how she handles, that would be nice.
Finally, if you actually buy the boat, develop a workplan of the repairs you want to do, starting with safety items, important mechanical items and eventually cosmetic/comfort items. And use this website for advice--there are lots of great experts here and they are friendly.
I know I've likely overlooked some key points, but others will also chime in and this will get you started.
Frank