How to blur the background of a photo
Select the subject, then use Iris, Tilt-Shift, Field, Lens or Depth Blur in Paint by Zaweba to soften the background and make the subject stand out.

Select the subject, protect it, and blur everything else. Paint by Zaweba offers several blurs made for the job: Iris Blur and Field Blur for a natural fall off in sharpness, Tilt-Shift for a band of focus, and Lens Blur or Depth Blur, which work from a depth map for the most realistic result. Several of them come with bokeh options, and you place them on a live preview.
A blurred background is what you get from a wide aperture lens: the subject is sharp and everything behind falls away into soft colour. Phones and small cameras often can't do it optically, but a careful edit comes close.
Step one: select the subject
The selection decides how good the result looks. Use any of the selection tools, and finish the edge in Select > Refine Edge, which handles hair with its Refine Brush. If the photo already has some depth of field, Focus Area can pick the in-focus part for you.
Save the selection or turn it into a mask. You'll want it again.
Step two: choose a blur
Iris Blur gives an oval of sharpness that softens towards the edges. You drag its handles on the preview to set where focus is and how quickly it falls off. It's quick and suits a subject in the centre.
Field Blur lets you place several pins, each with its own amount of blur, so the background can get softer the further away it is. That's useful for a scene with depth, like a path leading into the distance.
Tilt-Shift keeps a band sharp and blurs above and below, which gives the miniature model look when used from a high viewpoint.
Lens Blur takes its depth from the picture's brightness, a channel or a separate depth image, and has iris shape, highlight and noise settings. It's the closest to a real lens, especially when you build a simple depth map, white for near and black for far. Depth Blur works in a similar spirit.
Blur gallery handles are dragged on the preview, so you see the effect as you place it.
Step three: keep the edges clean
Blurring the whole picture and masking the subject back in can leave a halo, because the blur drags subject colours out into the background. To avoid this, work on a copy of the layer with the subject removed and filled from its surroundings, so the blur only spreads background colours. Then put the sharp subject back on top.
Getting a good result
Match the blur to the scene. Things near the subject, such as the ground under someone's feet, should be only slightly soft. Things far behind should be softer. Field Blur and Lens Blur with a depth map both make this easier than one even blur.
Add grain back. Blurring removes noise, so a blurred background can look unnaturally smooth next to a sharp, grainy subject. A light grain over the background, or over everything, makes the two match.
Watch the edges of the subject at full size, especially hair and hands. Soft edges look more real than razor cut ones.
Other blurs worth knowing
Paint by Zaweba also has Gaussian, Box, Motion, Radial, Spin, Path, Shape, Surface and Smart blurs, plus Bilateral, Zoom, Disc, Kuwahara and Variable Blur. Motion and Spin are good for adding movement to a background behind a moving subject. For the simple portrait look, though, a good selection and Iris or Lens Blur is all you need.