To avoid an unpleasing background, find a different angle for your shot.
Get down low to use the sky as a background (example above left).
Some of my favorite shots were taken while I was laying flat on the ground or floor.
Getting above your subject allows the lawn or even your carpeting (example above right)
to function as your background.
At your own risk of course, get up on a counter, step ladder, chair or other stable
object to get the angle you want.
Keep in mind that the background needs to have a complementing and pleasing color scheme. Clashing colors are clashing colors - avoid clashing colors. Find a different location. Your subject may need to select different clothing. This rule applies regardless of the background being in or out of focus.
Unless you are looking for a special effect, you need to be aware of the relative brightness of the background. There are exceptions to this rule, but having background objects that are brighter than the subject will often be distracting. Your eye will typically be attracted to the brightest part of the picture.
If you can't find the right existing background, add your own. Many backdrops/backgrounds are commercially available. A simple and inexpensive backdrop is a very large sheet of white muslin fabric. This makes a very pleasing background for portraits (example above). Build a PVC pipe frame to hang it over and you are set.
For a lower budget approach, employ a white or black sheet. Black velvet was used for the above/left baby picture - it makes a very nice background material. The above/right picture was simply a bed comforter. Be creative!
For a very low cost background, try construction paper. The background in this butterfly metamorphosis picture (above) is a piece of black construction paper.
Continued ... Digital Photography Tips - The Background (Part 4)