Few ideas:
- Run a network cable to a wireless access point int he shed (Cheapest and most reliable solution)
- Point to point wireless (Most expensive, least reliable)
- Powerline networking (Moderately priced, simplest solution)
First, if it can work, powerline networking is BY FAR going to be easiest thing to do. (not the best perhaps, but the easiest). It will only work if your shed isn't on a different transformer somehow. I'm not sure what the max distance is, but I think it is worth trying. Here's
some equipment to get your started.
The concept is simple: Connect one powerline broadcasting unit to your router and plug it into a power socket. Plug the other receiving unit (which can have wireless built in) into an outlet in your shed.. run the setup.. presto... instant wireless in your shed. It also works surprisingly well.
For the wireless solution... Assuming your shed is line-of-sight to your home, you can consider a point to point wireless bridge using two directional antennas to connect your home and shed together.
Since you cannot get a signal inside the shed (and even if you could, the signal would almost certainly be poor quality), the idea would be to mount two directional outdoor antennas outside. The one from your home would 'beam' the signal to the one outside your shed. Once the signal reaches your shed, you can connect that antenna to a wireless access point inside of the shed and enjoy wireless on the inside.
Code:
[Home Wireless]
|
(Cable)
|
[Home Antenna] >>> WIFI >>> [Shed Antenna]
[ or Wifi AP ] [ or Wifi AP ]
|
(Cable)
|
[Shed Wireless]
Outdoor antennas are more expensive and you might be able to get away with using an indoor antenna from your home but the receiving antenna for your shed MUST be outside since your wireless can't penetrate the walls. Again, if you can get the signal to the outside of the shed and collect it with an antenna, you can run a cable into a window or a hole somewhere that will connect that outdoor antenna to a wireless access point inside of your shed.
Just to get you started,
here are some antennas.
You could also (and this will be easier) invest in two outdoor access points with directional antennas.
Here's a little something to get you started.
Access points will be more expensive, but you won't have to worry about trying to rig up an external antenna on your router (may not even be possible for your router) and you'll be able to connect the wireless AP (access points) using standard CAT5/CAT6 network cable... this gives you more flexibility in placing your antenna too. You need it to point at your shed and you want it outside or as close to the shed as possible. Antenna cables have to be very short, but network cables can be very long.
The network cable solution: Despite wireless being a possible solution, I *strongly* recommend running a cable from your home to your shed (if at all possible). You can get up to around 300ft before extra equipment is necessary. If it is not possible though, then wireless will work if you get the right equipment. A straight cable is *always* better though. The idea is you'd run a cable from your home router and connect it to a wireless access point in your shed.
Lots of considerations

Good luck.