To join a Space simply click on the 'Join' button (right top). Any Space you have access to can be joined.
When joining a Space it is automatically added to your Home. In addition, you can now add/remove Guides*, add it to other Organisations, and you are listed as a contributor of the Space.
In an overview of all the Spaces of an Organisation it's easy to spot the ones that you have joined already, check out the grey user icon in the right top of the card:
Note that for every Space shows how many guides, people, and connected Organisations there are. In the example above 7 Guides, 217 people joined, and over 4000 (4k) organisations are connected to it.
*depending on the permissions set by the Admin