I finished work for a client a few weeks back called Duke of Hoxton. They are a clothing company based out of London, England.
This is roughly how the process went:
The client’s idea was to have the left side of the crest design more traditional posh British and the right side to be more “street” and rough. 
I haven’t done a more classic crest style in years, so this was interesting to get back into. We of course went through numerous drafts before the final version below was decided on…

Various versions include:

I decided on the final version because of the overal balance and how it best represented the 2 conflicting sides.
The pattern in the upper right really helped balance the contrast-heavy Union Jack in the lower left.

You can also see a number of variations on the main “Duke” character, I try to explain to clients why exactly I’m doing certain things with a design. I will sometimes include “bad versions” or “wrong versions” to illustrate why a particular idea or style doesn’t work, and pit it against the working idea. This way the client can decide for themselves what I already know :)

You can see I started off with a very different Duke character. Tried to make him more interactive, but he didn’t really blend too well with the overall flow of the crest, hung over edges etc.
I also tried various objects below the skull version of the Duke. The lower versions I tried explaining why something did or didn’t work well with the design, for example you can see on the very last one the balance between the golf club and tennis raquet are off, mainly because the sizing difference between the actual real life objects.

I also like to include dumbed down or simplified versions for usage on tags, tees or a more basic logo for a business card or website header.
I’m actually very happy with how these simple versions look, I think they hold up strong on their own.

These tee mockups were done post production, just as examples for my portfolio. 
I left the final layout and sizing up to the client, which I often try and do.

Thats just a very short simplified version of how the process works.
For a few tips on dealing direct with clients, you can read my old but still applicable Behance interview.