I use my Olympus 50/2 fixed-focus camera shot some chrysanthemum photos, the use of large aperture shooting, feeling the effects of grammaticalization background can also, don't know "DT" friends, do you feel?
There are a few things we can do to best throw the backdrop out of focus. If we do not have a fast lens, we can (1) select an angle of view where there are no distraction behind the subject i.e an open 'space' behind the subject, or (2) focus as close as possible with your lens to the subject, or (3) use the biggest aperture your lens have , or (4) if your lens is a zoom lens, try zooming to the furthest focal length to capture the subject. A combination of most or if possible all of the above mentioned should give a good OOF backdrop to your photo.