With the information you’ve provided your options are pretty much wide open. Here’s my top 4:
Option 1 – WiFi
This has the benefit of being easy & relatively cheap: Simply deploy a bunch of WiFi hotspots acting as repeaters to extend the range of an 802.11 WiFi network until all your buildings are covered.
You may need to invest in WiFi access points that let you bridge back to Ethernet, but those are pretty commonly available these days (pretty much any Netgear device will let you do it, I’m sure others will too).
As a bonus using WiFi means your open-air space will have a usable network.
Option 2 – Wireless Microwave (point-to-point)
Like option 1, but with more expensive hardware & requires a line-of-sight between buildings.
Microwave links can be very reliable if set up properly, and unlike the 802.11 network your bandwidth won’t be dragged down by the range extension & multiple clients mucking up the SNR. It’s a preferable solution if you’re doing stuff that’s bandwidth-intensive or latency-sensitive (like VOIP).
Option 3 – Cable (Cat5, Coax or Fibre) from building to building.
If your buildings are all in the same general area and you’ve got competent folks around you can simply run network cable (cat5 or cat6 shielded) from building to building, (ring or star topology is the best way to go) to extend your network. This requires lots of cable, and is subject to distance limitations which may make you have to switch to coaxial or fibre in order to make it work.
Bandwidth may be an issue here — Gigabit over copper will do for a lot of applications, but if you need more than that you would have to run multiple lines as a trunk, or use coax/fibre for the inter-building links (both of those should be fat enough to handle anything reasonable).
Option 4 – VPN Tunnels
This is really a great option if your buildings are geographically distant but each one has an internet connection — Simply set up VPN tunnels back to the network you need to reach. Note that VOIP and bandwidth-intensive stuff may kill this option.