Once your piglet is comfortable in the house, after a couple of weeks you can introduce him or her to the outside area.   As long as the fencing is secure, with no areas of escaping.. your piglet will do fine in the backyard 

It is nice to provide your piggy with a kiddie pool to lay/play in when it is hot outside.  Piglets can't hop into a kiddie pool, so we suggesting cutting out a nice wide "step in" for your piglet that is low enough for him to step into.  Or, get an extra litter pan (as listed above) and use one outside full of water for your piglet to get in and cool off.  This also serves as a simple way to ensure your pig does not run out of water or get overheated.  Our piggies here love to play in their pools. Since pigs do not sweat they have no way to cool off if they are not provided continuous water to drink. If you do not have room for a kiddie pool we suggest you either secure their water dish or use something like a ceramic one that is heavy enough that your pet can not knock it over. 

Outdoor pigs need a sturdy, rainproof shed, barn or doghouse. In cold climates, it must also be wind-proof and have enough room for plenty of straw and blankets to keep the pig warm. Ideally, outdoor pigs should be kept in small groups for extra body warmth. Remember pigs need plenty of fresh water at all times. In hot weather, they need a small pool or mud puddle to keep cool. In cold weather, be sure not to let their water freeze. It is not recommended that a pig be kept full time in a run or pen with a cement floor. 
A pen isn't necessary, you can have a nice secure dog house and shade in your backyard and that will be sufficient.  If you want to create a pen... it should provide the pig plenty of room to move around, and a place for its potty area away from its housing and food areas. We like pens no smaller than 8' x 16', with access to areas outside the pen for exercise.   Pigs don't jump high, but they do like to root & dig. A 4-foot high fence will easily keep your pigs in, but will not keep an aggressive dog or other animals out. If you live in an area with stray dogs or other roaming animals and creatures (i.e. kids), you may wish to choose a 6-foot fence. 

Hog panel (available from farm stores) is the best and probably most inexpensive and secure fencing material. These panels are used by commercial hog farmers and are good and sturdy, for making sure the pig stays in its pen. Chain-link fencing reinforced with chicken wire at the bottom may also make a suitable pen, but BE SURE there is no place a pig's snout can get stuck, caught or injured. Pigs are curious and will root and look for holes and ways to move the chicken wire. To be sure the pen is completely secure, you should dig a trench about 1 foot deep just inside the chain link fence. Fasten the chicken wire to the lower 6' of the fence and extend it down into the trench. Fill in the trench, burying the wire. You can also put boards into the trench, bury part of the board, and fasten them to the fencing to secure the bottom. Picket or split-rail fences will NOT keep a pig in, but you can attach a hog panel to the fence to secure it. That makes an attractive as well as secure fence! A board on board fence will keep a pig in, but may require reinforcement at the base, so a pig can't dig out beneath it.