The most effective way to non-destructively change the colors of objects and backgrounds in Photoshop on the Web is by combining Selection Tools with an Adjustment Layer, typically Hue/Saturation or a Solid Color layer set to a Color blending mode.

Here is a step-by-step guide using the Hue/Saturation Adjustment Layer, which is ideal for changing an existing color to a new one while retaining highlights and shadows.

1. Select the Object or Background
First, you need to isolate the area you want to change (the object or the background).

Select Tool: Choose the Object Selection Tool or Quick Selection Tool from the toolbar.

Isolate the Area: Click and drag or hover over the area you want to change to create an initial selection.

Refine: For a background, you often select the subject first, then go to Select > Inverse to select the background. You can refine your selection using the Select and Mask workspace (if available, or by adjusting the layer mask later).

2. Apply a Hue/Saturation Adjustment Layer
Once your object or background is selected, apply a non-destructive adjustment.

New Adjustment Layer: With the selection active, click the Adjustment Layer icon (half-filled circle) at the bottom of the Layers panel and choose Hue/Saturation.

Automatic Mask: A new Hue/Saturation layer will appear, and your selection will automatically be applied as a Layer Mask (the black and white thumbnail) to the adjustment layer. This ensures the color change only affects your selected area.

3. Change the Color
Use the Properties panel for the new Hue/Saturation layer to make your change.

Adjust Hue: Drag the Hue slider left or right to change the base color (red to blue, green to yellow, etc.).

Adjust Saturation: Drag the Saturation slider to increase (more vibrant) or decrease (more muted/gray) the color intensity.

Adjust Lightness: Drag the Lightness slider to make the area darker or brighter.

4. Fine-Tune the Effect (Layer Mask)
If the edges of the color change are messy, you can clean them up using the Layer Mask.

Select the Mask: Click the Layer Mask thumbnail (the black and white square) on your Hue/Saturation layer to select it.

Use the Brush Tool (B): Select the Brush Tool.

Paint with Black: Paint with black on the mask to hide the color change (and reveal the original color) in those areas.

Paint with White: Paint with white on the mask to show the color change in areas that were missed.

Alternative Method: Solid Color Fill
For a completely uniform color change, especially on a background, you can use a Solid Color fill layer:

Select the Area (e.g., the background).

Click the Adjustment Layer icon (half-filled circle) and choose Solid Color.

Choose your new color from the Color Picker.

In the Layers panel, change the Blending Mode of the new Solid Color layer from Normal to Color (or sometimes Hue or Soft Light, depending on the desired effect).

Use the Layer Mask to refine the edges as described above.