It does not matter if you are shooting in the garden or out in situ, the background is very important and an intrinsic part of the image. Always scan around the image in the viewfinder or on the screen before taking the picture and if you do not like the look of it, do something about it.
Changing camera position is the most obvious thing to do but you can just bring in your own background for times when this isn't possible. It can be a quick fix: a piece of board, a piece of card, a jumper etc. or more elaborate like a print with a suitably blurry background. That is up to you, but always consider the options when shooting. Do stay away from objects with a glossy finish, though, as you could get unwanted reflections.
In the shots below, the left photo is of bluebells in front of a greenhouse and even though the background is blurred, it's still a little messy. The middle shot shows the same flower but this time it was shot against a white polyboard and for the final shot a pink cushion was placed in the background.
It's worth noting that even though you'll be OK trying this technique in your own garden some public gardens and parks may not welcome it so do check before you start setting up your gear in a flowerbed.
You can hold the background yourself and set your camera on a tripod, using its self-timer to give yourself chance to get in position. However, it's much easier if you have a stand or spare tripod that can hold the background in place or have a friend hold it for you. That way, you can focus on setting the shot up and getting your camera settings right.
Do remember to check the frame before you hit the shutter to ensure the background fills. If, for whatever reason, this isn't possible, make sure there's room to crop the shot once in front of your computer.