I use Chrome and Yandex.Browser (basically a more private version of Chrome with a nicer GUI) and I want to be able to access the Tor network in these applications. I don't want a full Tor Browser to be running in the background as this would be inefficient, but I don't really know how to configure the Expert Bundle advertised on the Tor website. How could I do this?
Tor and TBB are two different things. TBB (i.e. Tor Browser Bundle) is a specific browser "adapted" for anonymity (e.g. hasn't 3rd parties that could leak personal infos), so Tor is just a proxy that already runs as a proxy.
What you've to do is just run tor.exe and check the output, if you find something like
[notice] Opening Socks listener on 127.0.0.1:9050 everything is done. If don't find this probably there is something wrong, so re-download the file and try again (because Tor by default open a socks proxy on localhost serving on port 9050).
But remember that this is not so safe, and this is why they made a TBB.
Step two, you've just to configure Chrome to use a proxy with
localhost as address and
9050 as port to point to.