Melissa is right on although I would temper one thing. Forget about explaining your situation and just send a friendly letter saying you are a new neighbor and just wondering if they have any interest in selling their land. The follow-up letter(s) are a good idea too because it may take them time to respond but once they do, then you can get into more detail if appropriate.
The fact that they are out of state is a good thing too. The next thing you should check is the Treasurer or tax collectors website for the county or city the properties are in. If they are delinquent in paying their property taxes then that's a good sign that they may be motivated to sell. This is where you should also be able to find the owner names and addresses
Next you will want to do some due diligence and determine the value of each property. I am in the vacant land business and here's what I typically do. Call the county or city Recorder, whomever holds the deeds where you live, and verify who owns the property, if there is a mortgage or not and what kind of deed they have (warranty is best). They may also have a plat map or survey for the property.
Next, call the county or city Assessor or go on their website where they should have a "property search" function. Enter in the parcel number or name on the deed and see what information they provide you such as assessed value, last sale, size, zoning, etc.
You could also call the Planning & Zoning or Building Dept. and see what the allowable uses are for that property's zoning designation. They would also be able to tell you about any future plans for the area.
Then, as far as price or value, you might ask the Assessor what their formula is for assessed value vs. market value as a starting point. Then hit the internet to check listings. Try the biggies, Zillow/Trulia and Realtor for agent listed properties and then the many other websites like Landwatch for FSBO lots. This will give you an idea what similar property sellers are hoping to get in the area.
Then, to get a true approximation of value, find a real estate agent who will search the MLS for actual sales. These are prices an actual buyer has paid and if there is enough data you will see what the market currently is. The Assessor may also have this information - maybe even on their website as some do now.
If the sellers are truly motivated (not paying taxes and out-of-state) you may be able to get their property for 10 cents on the dollar. Regardless, you want to leave lots of room between what the market will bear and what you pay to insulate you against unknowns. And last but not least, understand your exit strategy before you do anything and it will guide you along the way.
For more in-depth discussion on all this and much more I would refer you to Seth Williams excellent blog and website, retipster.com.