The simplest way to build an outdoor fireplace from an old indoor wood stove is to simply move the stove outside and place it in a location away from any combustible materials, removing the flue assembly to let its smoke rise directly into the air. This produces an outdoor firebox that will generate heat with the door opened or closed. If the wood stove is in disrepair, you can use sandpaper or steel wool to remove rust and corrosion before painting and sealing it with a heat- and weather-resistant finish.
You can turn your wood stove into an open fireplace by removing some of its components. The heat shield that protects indoor walls is unnecessary unless you place it against one of your home's exterior walls. The top of the wood stove, which may be attached with screws or may be part of the body's metal assembly, is also unnecessary if you want open flames to cook over. You can unhinge the door as well to provide open access to heat. Keeping the legs or pedestal and bottom shield will elevate your fireplace and keep the gravel or dirt below it cooler. If you want your fireplace to be at ground level, make sure you place a non-combustible material below it.
When you move an indoor wood stove outside, you'll need to be mindful of the fire's venting needs. The same air inlet will allow the fire to draw in air for combustion. However, venting smoke will need to be handled differently. If you keep the flue and damper attached, you can control the release of heat and smoke through the top of the fireplace. However, the flue will become extremely hot during use, which means you can't simply run it along an exterior wall. If you plan to build a fireplace on an outdoor deck or patio, you may need to install a new chimney or locate the fireplace away from your home at the far end of the deck.
An old wood stove can become the center for a traditional masonry outdoor fireplace. To produce this type of fireplace, keep the wood stove largely intact, removing only the door and heat shield. Mix up mortar and use it to construct a freestanding brick or stone shell around the wood stove body, including a masonry chimney that surrounds the flue. You can add a mantle or new doors to contain the fire and give the fireplace a more finished look.