Building a bathroom in your basement is an excellent way of increasing the value of your property. However, since basements tend to be underground by definition, this can create problems. Fitting a bathroom is possible to do yourself, at least the majority of the work.
However, you will have to do careful research on both your property and the kinds of fittings that you're using before you commit to doing the work. If in doubt, always consult a plumber or bathroom fitter, because badly fitted bathrooms can result in water and sewage leaks...
Determine Your Drainage Line...
Before even thinking about starting to fit a bathroom, you need to determine where the drainage line is for your property. In some cases, particularly for houses that half half basements (where the house is built on a hill, so only part of the basement is underground, and at least one full wall is above ground), the drainage-line will be under your property, including the basement.
You need to find out where the main drain exits your property. If you're unsure about this then either consult the plans of your house, if they're available to you, or ask a plumber. If you have floor drains in your basement, there's a good chance that the drainage line is under the basement.
This means that you will have no problems fitting a bathroom. However, the majority of full basement houses (where the entire basement is underground) have their drainage lines about half way up the wall of the basement. This means that you're going to have to find a way to get water and sewage up from the floor of the basement to above the drainage line so that it can drain away through the main drain.
Up Flush Toilets and Macerator Pumps...
There are solutions if your drainage line is above the level of your basement floor. Basically, what you need to do is to create a drainage chamber under the bathroom floor, and then use pumps to get the waste up and out of the chamber and above the drainage line. This is obviously a more complicated way of building your bathroom. However, without doing this, your bathroom will never work.
You will probably need two different chambers and two different kinds of pump in order to do this. Sewage will require a macerator pump, which is a pump that breaks up solid matter so that it can be pumped upward. Water requires a simple pump.
You can combine these and use only a macerator pump to do both jobs, although it's worth remembering that macerator pumps are expensive, and by making your macerator pump work for the whole system you may be placing it under undue wear and tear.
It may be worth dividing your chamber and having a section for waste water from the sinks and shower with a normal pump, and a section for sewage with a macerator pump. That way the macerator pump works only when it is necessary and will last longer before it needs to be replaced.
Specially designed up flush toilets ofter contain their own chambers and macerator pumps, which is another option for you. It's usually a good idea to have pumps installed by a professional, since they deal with water but are usually electric powered.
The combination of water and electricity is dangerous if pumps are badly installed. Installing a bathroom below the drainage line of your property will certainly be more expensive, and will probably require professional help, but all of this will be reflected in the increase in your property value.