The aperture controls the amount of light that can come through your lens, it consists of blades that can narrow the 'hole' in your lens. You can see it in the pictures above. The size of the hole is indicated by the f-number, the smaller the number the bigger the hole (this might be a little confusing at the beginning). So f/4,5 is bigger than f/29. The size of your aperture influences the depth of field. You can see this in the photos on the right. So if you want everything blurry except for your subject, choose a low f-number.
All DSLR's have an option to set the size of the aperture, mostly its called aperture priority mode or just A. Some compact camera's have this option too, Phones however never have this function because they have a fixed aperture.
The closer you get to your subject the blurrier the background will become.
3. create a bigger distance between your subject and the background
This will make the background less in focus and therefor less sharp.
When you zoom in on your subject the effect will be similar to getting your camera closer. This only works with optical zoom (when your lens gets larger) and not for digital zoom (the thing phone camera's do when they zoom in). Digital zoom is just cropping your photo and doesn't change anything about the depth of field.
The size of your sensor has huge impact on your photo quality, and also on the depth of field. The bigger the better. Phone cameras have really small sensors, compact camera's a little bigger onces and DSLR's have quite big onces. In the picture you can see the different in sizes of phone and slr camera sensors.
You can also blur your background with some photo editing. You can do it with photoshop, instagram, picmonkey and numerous other apps and programs. But as you can see in the photo above is the blur different. Personally I think real blur to be much prettier. With real blur I mean blur that is created by using one of the other options in this article.
Free lensing is an awesome technique you can try with cameras that have interchangeable lenses. I wrote a post about how it works a while ago. Free lensing can make the depth of field very narrow. It has the same result as a tilt and shift lens but those are quite expensive.
I hoped this helped you guys! If you know an other technique on getting a shallow depth of field please share it in the comments, I'd love to learn more!