You can make your own fireplace, but you should make sure that the fireplace does not interfere with load-bearing walls first. Since an exposed chimney has to be cut out of the wall or vented through the corner of your house, you want to be sure that you will not accidentally set the house on fire or reduce a wall's ability to support the upper story and roof of the house. Once you have figured that out (a structural engineer can help), then you can construct a fireplace using one of the two following methods.
Traditional Brick Fireplace and Chimney
A traditional brick fireplace and chimney is easy enough for a beginner/amateur mason such as yourself. You need to cut space within the designated wall for the chimney. The chimney is the rectangular tower stacked on top of the box-shaped fireplace. Start by making an outline of the fireplace, using bricks and mortar to secure the bricks to each other and to a concrete slab that makes up the hearth. (If you need help pouring the concrete slab for the hearth and foundation of the fireplace, get professional help from a contractor for this part, and then do the rest on your own.)
Continue making mortar and brick layers to build the fireplace up. Once you get to the top of the fireplace where the mantle goes, you can choose to continue with brick, or install a pre-poured and formed concrete slab for the mantle. You could also use a granite slab, which is more decorative and will acclimate well to the heat of the fire. Except for the opening of the chimney, close off the rest of the top of the fireplace, both outside your home and inside too. Using a ladder outside, continue to build the chimney upwards using layers of brick and mortar. You will need a damper for the fireplace, so make sure you install that as you go. The project is complete after you finish off the top of the chimney.
The Messier River Stone Method
Some people tend to think that the river stone fireplaces are easier to construct. After all, you create a wooden structure and form into which you pour wet concrete. This method is actually trickier than it seems, since you have to wait until the poured concrete is somewhat firm and very unlikely to slide or run when you pull the wooden form partitions away.
Once the concrete starts to set, you pull away most of the wooden form and begin pushing chunks of river stone into the concrete. Continue pushing the stones into the concrete all the way up the front of the fireplace and chimney. You can do this to the outside as well, but because this is more decorative than functional, it is entirely optional.
For more information or advice, contact a business such as Alpine Fireplaces.