I have been using this lens for a while, mostly for portraits and have noticed that for some reason the outdoor pictures where I most likely had to quickly compose and take the shot have had something wrong with them.
Usually the image is out of focus and not as sharp as I have seen on other pictures.
Are there any tips to using this lens and is there a preferable operating aperture to give the sharpest photos?
There are many factors influencing sharpness and perceived sharpness. Without any concrete example it is hard to give a precise answer, but you might want to consider looking at Why are my photos not crisp? and Why am I having trouble getting sharp results with my new DSLR, compared to a point and shoot? in order to eliminate some of the most common factors.
Note that the lens gets very good reviews at http://kenrockwell.com/nikon/5018daf.htm and http://www.slrgear.com/reviews/showproduct.php/product/97 in particular regarding sharpness, but keep in mind that the Nikkor 50mm f/1.8D is probably not very sharp at f/1.8 (especially off the center) giving the image an overall soft look. At f/1.8 you also have a very narrow depth of field, thus making it hard to get the focus right (see also Will using a lens at max aperture ("wide open") result in poor images? and Is it difficult to focus on 1.4F prime lens, and if it is how to counter that? ). So, try stopping the lens down to at least f/2.8 or even more (look, e.g., at the sample pictures in the links above which are at f/8). Note that if using maximum aperture is the cause of your problem, then buying an even more expensive lens (which would probably be a 50mm f/1.4) might even make the problem worse.
There might be several reasons why you seem to get more "keepers" from your kit lens. One of them might be that the kit lens's widest aperture is around f/3.5, giving it a wider depth of field and thus making it easier to hide focus mistakes (see links above). Another reason might simply be that you have more experience and practice with the kit lens.
One simple experiment you might want to do is taking pictures of the same scene at, e.g., f/1.8, f/2.8, f/4, and f/8 and compare them. Also, after taking pictures, use your camera's display in order to check whether focus is really where you intended it to be (zooming in to the part that you focused on), and you should see that at in particular at f/1.8 this might not always be the case. Finally, try to get as much practice as you can with your lens, in particular in situations where there is enough time to carefully compose, check settings and results, and retake pictures if necessary. This will give you a better feel for the lens and help you deal with situations where there's more rushing necessary.
It sounds like it is most likely a user error, but it's impossible to say without samples.
Outdoor shots should be the easiest for the camera and lens since light is abundant and using a wide open aperture is not needed. The more light available, the easier time auto-focus has as well. It is possible that it could be the lens is stopping down too much and hitting diffraction problems, but that seems unlikely given your description of the problem.
If your subject is moving and you are using one-shot AF, this may also be part of the problem. Servo AF allows for the focus system to follow a moving subject, while one shot will stop trying to focus once focus is initially achieved.
The number one best way to make sure that you get fewer bad shots is to take more time and care when taking the shots. Make sure your exposure adjustments are where you want and that focus and composition looks good before you capture the image. A camera is just a tool and is only as good as the craftsman using the tool. Develop your technique and practice to get more experience and the quality of your shots should improve as well.
