I've seen many schematics online that are similar to mine. Can you provide an example of a well-designed schematic?

In the first one labels are used for the power and ground lines, but not much else. I'm not sure why the 24VCC line is highlighted, but you wouldn't normally do that. Note how you can follow all the signal paths easily, without having to search for labels.

The second one looks horrendously complicated, but in fact is easier to follow than if extensive use of labels had been made. The signal flow can be followed directly, rather than having to search all over the diagram for labels.
This is an important point: to you, that schematic probably looks scarily complex. But don't let that put you off. The question is, can you actually follow it? Can you trace the signal paths between the components? Can you see where the signal path splits to feed two components? Obviously in order to fully understand how it functions you need to look up the data sheets for the ICs, but that's true of a label-based schematic as well.

In the third one, it uses labels, but (apparently) only for off-board connections. To the left of the diagram you will see how buses have been used to simplify the diagram without making it significantly more difficult to follow.
I'm sure my examples will attract critical comments, but I just wanted to illustrate how even complex circuits can be drawn without widespread use of labels. In reality your circuits will be simpler than these to begin with. Here is a nice simple one.

Back in the day it was common to draw the ground as a horizontal line along the bottom of the diagram (thus Vcc across the top, ground along the bottom, conventional current flow downwards from top to bottom). Nowadays it seems more common to replace the ground line with ground symbols. I think that's OK, and it allows for signal lines to travel underneath the other components, as you can see to the right in that final diagram.