DISCLAIMER: I am a licensed Texas real estate agent.
I am not going to recommend that you contact a real estate agent or attorney first.
Several people have given you good advice about approaching the neighbor casually and I agree with them as long as you feel the neighbor is approachable.
One scenario where having a real estate agent talk to them first is if you think they may demand a premium price because they know the land is worth more to you than it would be to someone else. For instance, if the land would give you easier access to a highway from your property, or you have them surrounded on 3 sides and need their property to "square up" your land, the land they have used to belong to your family and you want it back for sentimental reasons, etc. In a case like this the agent can present an offer as a "Trustee" and your name would be left out of it.
If none of the above paragraph applies then approach them yourself but do not express any sense of urgency. Be very casual. "If you ever decide to sell your land I would be interested", not "I want to buy your land".
If the land is not being used you could offer to lease it for a while provided it is usable for your purposes without a lot of work. You don't want to improve their property for them, that would drive up the sale price later on.
If they don't want to sell now you could offer to pay them for "First right of refusal". That means you would pay them $X and have a contract drawn up that says that if they ever decide to sell they can put it on the open market. When they get an acceptable offer then they have to come to you and offer to sell it to you for the same amount. At that point you can either buy it or, if the price is more than you are willing to pay, you can pass on it and the other buyer gets it.
If they are older folks who want to keep it for the rest of their life but don't want to pass it on to someone in particular you could offer to buy it on a "Life Estate" basis. That means you pay them for the land but they get to retain possession of the land until they die or decide to move on at which point you then gain possession. This can be useful if they need to money to supplement their retirement income but don't want to give up the land.
As someone suggested, if they are in a tax bracket where they would be hit hard by the monetary gain no the sale you could offer to buy it on an installment purchase. This would also be a good way for them to sell it if they are financially set and are going to put the sale proceeds in savings. At todays interest rates they will do well to get 3% for the savings. You can offer 6% interest and they will realize a better return on their savings.
There are more options to buying property than an outright cash (or third party financing) sale.
In any case, if they agree to sell you can pay a real estate agent to write up the formal contract. Every time I have seen an attorney try to write a sale contract for real estate they got it so complicated that the seller would often refuse the offer because of all the legalese and terms the attorney would put in.
Real estate agents have standard forms that are written by their state association lawyers that are much more "user friendly" and easier for both buyer and seller to understand.
Lawyers do not have access to information about other recent land sales in the area but real estate agents do have access to that information. This information is critical in deciding if the price is fair or not.
Whatever you do let me give you some very important advice: NEVER, EVER, buy any property without getting a title policy! I have seen sales where the buyer ended up losing the property (and the money they paid for it) later because of a "cloud" (encumbrance) on the title. There are also case where the buyer had to pay for the property twice, first to the seller and later to some lien holder who they didn't know about when they bought it. A title policy is an insurance policy that will pay you up to the amount you paid for the property if the title is not clear even if the encumbrance doesn't show up until years later. Since insurance companies don't like to pay off they research the title history to be sure there are no liens or other problems.
Have the property surveyed before you close the sale. Lots of fences are built that are not on the property lines. You may think you are buying 14 acres but only a licensed surveyor can tell you how much land you are really getting and exactly where it is located. That's why you will always see land advertised by agents as "14 acres +/-" or "14 acres more or less". Nobody knows exactly if it is really 14 acres or not until it is surveyed.
I have seen lots of problems with titles, surveys, etc. For the most part they are easily cured (solved) as long as you use the right professionals.
BTW, real estate fees are negotiable. I have often written sales contracts for a "fixed fee" when the buyer and seller had already worked out the details of the sale. I based my fee on the amount of work they wanted me to do. Be specific about what services you want the agent to perform. Do you want them to just write the sales contract or do you want them to also review all the closing documents including the survey? Do you want them to attend the closing, etc.?
I wish we could all still do business on a handshake but we can no longer do that. For instance, I wanted to buy some land around my place. The seller was willing but his daughter decided she "might" want to build a home on that land someday. Fat chance, she lives 1,500 miles from the land and to my knowledge has never even seen it. In this case I believe she just didn't want him to sell it and spend the money. She wanted to wait until he died so she could inherit it and then sell it and get the money for herself. Kids can be awfully greedy when it comes to inheritance, even at the expense of their own parents.
Sorry this is so long, but life has gotten awfully complicated in the 59 years I have lived on this planet.
Bill Tolle
Kubota
B7510 w/FEL and 3.2 hours on the meter!