Start a new project in Photoshop. You can do this by dragging the image you want to edit onto the main menu or clicking Create new... on the left.
If you want to blur the background of an existing image, import it into Photoshop. You can drag and drop the file onto the workspace or use File > Open to find the image on your computer.
This process can be easy or difficult depending on the image you're trying to edit. There are many ways to go about making a selection in Photoshop. Different tools are ideal for different types of images and textures.
For example, the Wand tool (press W on your keyboard to activate it) works best on solid colors with little texture. The Lasso tool (press L on your keyboard) is great for manually selecting portions of a photo.
Use whatever means you prefer to select the background.
If you refine the edge of your selection, the changes you make won't be obvious by leaving hard pixels. There are several ways to go about refining a selection edge; my favorite is to feather it slightly.
After making a selection, go to Select > Modify > Feather. This will open a pop-up menu. Play with the settings to optimize the edge of your selection. You may have to experiment to get the effect you want.
You have many options for blurring in Photoshop. There are tools and filters designed to create a variety of blur effects. My go-to method for a quick blur is the Gaussian Blur tool. You can find it under Filter > Blur.
This menu has additional blur tools, each with a variation or twist for a unique effect. I can't say this enough—experiment until you find the exact effect you're trying to accomplish.
Once the image background has been sufficiently blurred, save the changes under File > Save or otherwise continue working on your project.