The ways an RVer can connect to the Internet are via Cell Phone, WiFi or Satellite Internet.
None of the above are that easy and all take some work to explore the options best suited for you. These days some of the RV campgrounds have installed WiFi and you can expect many more to so over the next few years.
A good book to learn all about it is RVers Guide to Internet Access On The Road.
There is also a blog: RV Internet Access that makes interesting reading.
A list of RV campgrounds with WiFi: RV Park WiFi Hotspots.
If you want to use your laptop in your automobile you need a power inverter.
An inverter converts the DC power generated by your auto battery into AC power needed by the laptop computer. These devices will plug directly into the cigarette lighter in your car and allow you to connect the power plug from the laptop's AC adapter into the other end of the inverter.
There are two types of inverters: modified sine wave and pure sine wave. The AC created by the modified sine wave may not work well with some laptops, so check your user manual.
Laptops require 50 to 75 watts of power. You should purchase an inverter that provides 10 to 20% more than your largest load. Most auto batteries will provide 30 to 60 minutes power, even with the engine off.
If you plan on regularly running off the auto battery, you should plan on getting a quality inverter from a company like Xantrex. They have sold over 200,000 inverters to the laptop manufacturers. Their StatPower PW-50 or 75 or the Prowatt 150 would be a good choice for occasional use. Prices range from $40 to $70. If you plan on using it frequently, a pure sine wave inverter from Simlex (PST-15S-12) for around $120 would be a good choice.
Some laptop manufacturers also sell an auto adaptor that will allow a laptop to run on 12V. I suggest you do your research. You may find it costs less to buy a small inverter.