Sub collections are not natively built into Shopify, meaning we need to be creative in order to output these.
There are many ways to go about this; including using naming conventions when setting up collections as well as concatenating tags.
In my opinion tags are the best way to create sub-collections, this ensures you always stay "within" the top level collection and you can create a more automated system. This option defines the sub collection structure within the tag.
For my example the products is going to be a Women's shirt. I have created a collection called Womens already, all products of the type Womens will go into this collection.
We also want the product to show up under both a second level collection "Clothing" and a third level collection "Shirts". To get this to work without having to create collections we would tag the product with both: Womens - Clothing and Womens - Clothing - Shirts
The first part of the tag must match the top level collection name.
We then need to set up a link list called "Collections" which will include each of your top level collections.
In my example I have set up a sidebar on the collection pages. Add the code from this gist to your sidebar snippet.
After adding some more products within both Womens and Mens collections, this is my final result: