There's really no single approach to creating sub-brands, but here is how the process might go...
- If you are creating the parent identity, then you're also taking into consideration how the sub-branding might work/look
- You experiment with slight modification of fonts, colors, imagery, etc of the parent brand and use your judgement to know if you've gone too far
- You submit your ideas to the client and rely on their feedback to know if you've gone too far; sometime they might be wrong, and sometimes not
- Repeat from step 2 if required
The exact changes to fonts, colors, imagery, etc should not be so extensive as to contradict the parent brand, but they should definitely have their own flare.
I have seen some companies adjust their logo for sub-brands by simply shrinking the icon, and adding some colorful text below the company name. Sometimes the text is a similar style to what the parent is using in its name, and sometimes the style is more customized towards the target audience (e.g., a more playful text for kids).
If you're dealing with printed materials, then it might be a good idea to create a master layout, and customize rather than reinvent for each sub-brand. Again, you have the same tools: fonts, colors, imagery, etc. You should also think about referencing the parent company with their logo somewhere, possibly near the bottom/end of the document.
For websites, you can use sub-domains (e.g., graphicdesign.stackexchange.com, vector.tutsplus.com). And once again, you have the same tools and you might want to create a master layout as well as include the parent company logo somewhere.
I think the key is to make sure that the result achieves the goals of the project. Sometimes companies actually want to distance the parent company from the sub-brand so they can enter new markets that the parent company would never be successful in. So the degree of changes will depend largely on the objectives of your client.