Adding a Daytime Sky
Taking a good photo is beyond the scope of this tutorial, but once you've got one that you've satisfied, it's time to fire up Photoshop:
After you've opened up the image in PS, the first thing to do is to unlock the lone layer.
The layer appears in the bottom-right corner and will have a little lock next to its name. Double click the layer, and a dialog box appears.

The window is entitled, "New Layer", but, nevertheless, this box applies to the existing layer. If you want to rename the layer to something meaningful, like "LEGO", you can do so here. Otherwise, you can be lazy like me and just leave it as "Layer 0". (and you can always rename it later if you're getting confused by all the layers, of course)
Before you go any further, now is the time to make any tweaks to the colors of your image. I usually increase contrast a bit and adjust the blues (and reds if there're any red, brown or other warm-colored bricks) in Curves, and make the yellows brighter and more yellowish in Selective Color.
Now, to the sky. Switch to the Wand tool by clicking the little wand or by hitting the 'W' key.
Start by selecting a patch of the blue backdrop. You can always add to this selection, so don't worry if you don't get all of the background, and don't go crazy increasing the tolerance to try to select more of the background. (I've set my tolerance to 30 for this selection)

Now hold down the 'Shift' key while you continue clicking until the rest of the sky is selected.

If you catch a bit of the LEGO, like I did with the wall here right above the bucket, that's okay. Switch to the Lasso tool...
...and zoom in to the problematic spot. Hold down the 'Alt/Option' key while you use the Lasso to remove what you select from the existing selection.
Yes, I could go with a mask here or use the Pen tool to get more precise, but there's really no reason to do that when you're making an image for the web. (and remember, the edges don't have to be perfect when creating this sky, because the edges are already bluish from the blue backdrop) Just use the Lasso to clean up the selection where you need to.
Navigate to
Select > Modify > Contract.
Contract the selection by a couple pixels. Now, my image is still at its original size, so the amount of contraction needed will depend on the size of your image. I've contracted by 2px for an image that's around 4000px wide, so you'll want to adjust that ratio depending on the size of your image. If your image is smaller than 1000px, I would just skip this step and move to the feathering step. If your image is around 2000px, I would contract by 1px, if your image is around 6000px, contract by 3px, and so forth.

Again, those edges are already bluish, so we don't need to cover them with this selection. Pulling back a little and then (as we'll do in a moment) applying a slight feathering to the selection will result in a better transition.
Navigate to
Select > Modify > Feather.
Not too much is needed. Just a feathering of one pixel for me. Again, this amount depends on the size of your photo. If your photo is smaller than around 2000px, I'd go with 0.5px. If it's larger than the 4000px I have in my example, then go higher than 1px.

Feathering is just a blurring of the edges of a selection. This will smooth out the transition and make it more natural and realistic.
Click on the square displaying the foreground color to set it to a new color. This doesn't actually change anything in the image; there are just two colors there - one in the foreground and one in the background - for things that requires more than one color, such as gradients.
Set the foreground color to whatever color you want to use for the sky. I like
#b0f0ff.

Now, create a new layer. (don't deselect the selection of the sky; we're just going to move to another layer before we fill it in)
Click the button that looks like a square with its bottom-left corner flipped up, and a new layer will appear above the old one.
In this new layer, go to
Edit > Fill.
The only option you might need to change is the first drop-down menu.

Just make sure it's set to "Foreground Color". (which you've already set to your sky blue)
This will fill the selection with that sky blue color, and your sky should look something like this:

And that's your finished sky. At this time, I resize the image to 800px wide before moving on to the sun and clouds.
Adding a Daytime Sun
Once you've got your sky finished, switch to the ellipse tool by clicking the shape or hitting 'U'. (you might have another shape tool loaded instead - just click and hold down to reveal the sub-menu or hold down 'Shift' while tapping 'U' to cycle through the various shape tools)
Set the foreground color back to white (#ffffff), and, in a new layer, draw a white circle. (hold down 'Shift' while drawing the ellipse to constrain it to a circle)

It doesn't matter where you draw it, as long as you aren't cutting off parts of the circle by drawing beyond the edges of the photo. If you don't know how big you want the sun to be, better to go bigger. You can always make it smaller later.
In the layers sidebar, click the button at the bottom with the 'fx' on it and choose 'Outer Glow'.
In the resulting dialog box, click the square with a solid color in it. (these glow settings were what I set as my default setting during a previous edit; your settings may not be the same, and you don't need to make them match at this point)

In the Color Picker, set a pale yellow.

Now, just fiddle with the settings of the glow until you're satisfied with it. I've set mine for a smaller and slightly concentrated glow that almost blurs the line between the white ellipse and the glow itself.
Apply the effect, and you're done:
Adding Daytime Clouds
You've got your sky composited in, and you've added the sun, but perhaps this isn't a scene on one of those days with perfectly clear skies. Time to add some clouds.
In a new layer, set the foreground color to black and the background color to white. Since these are the default colors, you can also set them by tapping 'D'. Now, navigate to
Filter > Render > Clouds.
Grayish clouds should appear over the entire photo. Next, go to
Filter > Render > Difference Clouds.
And then render those Difference Clouds a second time. (you can repeat a previous effect by pressing Command/Control+F) The rendered clouds are unique, but you should have something like this:

Now, navigate to
Image > Adjustments > Levels. (or use Command/Control+L)

Drag the little white arrow to the left to 'solidify' the clouds, and then drag the little grey arrow to the right to increase the black space between the clouds. There're no exact settings; just drag them back and forth until you've got something like this:

Now, in the layers panel, right-click on the layer with the clouds in it and select 'Blending Options'.
In the dialog box that pops up, change the Blend Mode to 'Screen'.

And now you'll see that the black areas have become transparent, letting the rest of the photo underneath show through and leaving only the white clouds on top.

You probably didn't get all the clouds right where you wanted them, so use the Lasso tool to loosely select one of the larger clouds that you want to move.
Now navigate to
Edit > Cut (or Command/Control+X) to remove it from the layer, and go to
Edit > Paste (or Command/Control+V) to place it in a new layer.
That's going to leave a big ugly chunk of clouds on black in the middle of the photo...

...but that's okay. Just change the Blend Mode of this new layer to Screen and all the black will disappear.
Use
Edit > Transform > Rotate to reposition the cloud.
The cloud will appear in the middle of a box with squares along its edges.

Click and drag the squares to rotate the layer, and click and drag inside the box to move it around. Once you've got the cloud repositioned to your liking, press 'Enter'. Repeat this cutting, pasting, and repositioning for all the clouds that you want in different places.
Now, in the layers panel, set all but one of the cloud layers to invisible by clicking the eyes next to the layers.
With the remaining visible cloud layer selected, click the button at the bottom with the white circle in a grey box to add a Layer Mask to this layer.
Click on that white layer linked to the cloud layer to edit the mask. Layer masks basically turn everything you paint black invisible, while everything painted white stays visible. So, switch to the Brush tool.
And in the top bar, open this drop-down menu to choose a specific brush.
I like to just use a large, soft, basic brush for this, like the default soft 100px brush.

Now, just brush over all the cloud that you want to get rid of in this layer, switching to a smaller brush if you need to get into smaller spaces between clouds:

Set the next cloud layer back to visible, add a Layer Mask, and brush away what you don't want. If you mask over something you wanted to keep, change the foreground color to white and use the brush to make parts of the layer appear again. Repeat this for all the cloud layers.

And that's your finished daytime sky, with sky, sun, and clouds.