How can I connect to a WiFi that's 500 metres away?
Solution 1:
500 meters, even 300 is much too far to be in usable range for WiFi. WiFi is designed to, in the best case, transmit throughout one small household. Also, physical barriers, like walls, cars, other buildings will severely degrade the signal. You might be able to get WiFi through one or maybe even two walls if you're lucky, but to get it 500 meters, you'd have to transmit at power higher than allowed by the standards bodies (and likely your government), and use an extremely directional antenna, with line of sight (no barriers in between).
The solution is probably to get your own Internet connection rather than trying to use theirs. You could also obtain a line of sight between your property and theirs (likely by building a small tower on your roof; check local regulations) and set up a very high frequency point to point link, but since you seem totally new to wireless communications, you (honestly) probably do not have the expertise to set one of these up even if you knew what you wanted, and would have to hire a contractor to design, spec out, price, and install a system for you, in which case you're better off going and asking an actual expert instead of asking us.
Lastly: the cost of custom designed radio communication systems like the ones I am talking about (which go above and beyond "WiFi") is often in the tens of thousands of dollars (or at least 7000 British pounds or so), not including labor. At that price, it is almost certainly cheaper (over a period of, say, 5 years) to pay for ADSL or cable Internet connectivity to where you live.
Solution 2:
This can be done at your in-laws' house and pointed to your house: Lifehacker Post DIY Wi-Fi Antenna Cheaply Extends Your Wireless Network
Or at your house pointed to your in-laws: Lifehacker Post Make a Long Range Wi-Fi Extender out of a Coffee Can
Both of these are not too technical and are very cheap!
Solution 3:
First off, you would need to measure how far from the router you want to be able to access the wifi.
Wireless G can reach between 38m (indoor) and 140m (outdoor). This range is affected by line of sight, meaning if their are any walls between where the router is and where you want to access it, the range decreases.
Wireless N can reach between 70m (indoor) and 250m (outdoor). Again, line of sight affects this range.
The average consumer-grade wireless router has been Wireless G, but more and more routers are moving to N, is it possible to update us on which standard they are using?
If the router sits towards the back of their house, you could invest in a wireless range extender, which would need to be connected to their network and placed towards the front of their house to get the maximum effect. This location would preferably be outside of the building.
Directional vs Omni-directional antennae will also affect the signal distance. A directional antenna would be best in this case, as it directs the majority of the signal in one direction. The standard antennae on a router, however, are omni-directional, meaning that they send out this signal in all directions.