If you are not using G+ on a mobile device, you are currently limited to setting the location as simply 'where you live' in your profile.
You can see where other people are though (if they're sharing their location with you or publicly) by visiting their profile; at the top you well see their current location and if you put your cursor over the location you will see a map.
Feel free to test on me!

Yes, understand that. But how does it work with a compatible mobile device? Does your location get updated automatically, can you just set the location with no other activity, or do you have to create a G+ post to set it?

Using the G+ Mobile Web interface in Chrome on an iPod Touch, Check in seems to create a G+ Post. There's no other obvious way to set location.

Checking in will not set your location for others to see aside from on that post I understand.

+Julian Bond if you enabled Location Sharing in Google+ and Location History and Reporting your current city wide location will be shown. You are able to set this to be only viewable for a certain circle or person. 

You are also able to show your pinpoint location and again for those you made it viewable for will able to see it, both on Google+ as through Google+ Locations. 

https://support.google.com/plus/answer/2998354?p=plus_location&rd=1

(For questions about Google+ features it's recommended to visit the Google+ community which is focused on helping and answering questions. This community is more focused on discussing upcoming features or report them)

Ok. Apologies for maybe posting in the wrong place. However, location support is fairly new to Android, new to iOS today and a feature request for desktop web. And frankly it's a feature request for mobile web as well since it's somewhat flaky there.

I'm being a little awkward but this "Google+ Locations" you speak of. URL? Or is this also an Android/iOS only feature?

I can go into web settings and set location history and reporting but frankly it's pointless since I have no way of setting it.

To try and make myself clear. I'm not looking for support. I'm trying to understand what is currently possible and currently missing so I can make a reasonable feature request.

Google+ Location is only accessible from mobile devices. The web feature like we knew it from Latitude is gone. So you won't be able to access from a web browser.
If and when it might return is up for speculation. 

Location sharing can be set from the web (Google+ settings) or your mobile device. Location history and reporting can only be set from your mobile device. If you have more than one device only set one of them to reporting or your location history will bounce around. 

On Google+ if the person has decided to share their location you have to go to their profile and you will get an estimate location of where they are if you over an area in near their cover photo. 

The link in my previous comment should give a decent explanation of what Google+ location is. 

OK. Thanks for that. So to go back to my original question. Is this right? 

Location sharing control can be set on all platforms. 

Posting your location is possible
- in background on Android and iOS,
- while posting a G+ post in Mobile web
- not at all on desktop web
This is the one I'm really interested in. Is this right? And why can't I do this when using the Mobile Web interface from Chrome on Win7? And as a future request, I should be able to do this from Desktop web.

A display of location is available
- On profiles on all platforms
- On a map of friends in Android and iOS

Nearby posts is available on Android, iOS and Mobile web but not Desktop web

So here's the feature request. Consistency! With equal location function available on all platforms as far as possible. 

Sharing - Yes
in the background - it automatically shares your location if set to do this
while posting - you have to choose to add your current location
desktop - correct, you can't post your location from the desktop web. Wasn't possible on Latitude as well but requested a lot.
Location on profiles - yes visible across all platforms
Map - correct, those that share their location with you, be that only the city or pinpoint location. 
Nearby - correct

Consistency is a request we all have with all Google products. Latitude only got shut down a few months ago I'm giving the old team time to adjust to the new "environment". 

Another bit of weirdness. If I view the plus website through desktop Chrome but with the iOS Chrome user agent, I get the mobile Web version and can check in/add location to posts. But if I connect to the mobile web URL with the default user agent, I get the mobile website. I still get nearby but I don't get check in or location on posts.

Gah!
Consistency!

Could you report that through the app so the team can get that. That's really weird

Done. Note:- - Chrome (31.0.1650.57) on Win 7
- Mobile interface at https://plus.google.com/app/basic/stream and https://plus.google.com/app/basic/share
Messing with the user agent via https://chrome.google.com/webstore/detail/user-agent-switcher-for-c/djflhoibgkdhkhhcedjiklpkjnoahfmg?hl=en-US&gl=US

This seems to have changed again. I'm sure it was possible for a while to set one's location via the Mobile Web UI such that the current location on profiles changed. I think this was either by making a post or a check in with a location attached. But no matter what I do, my profile seems to say "Lives in" rather than "currently in".

It's now 6 months since Latitude closed down. It's still not possible to set your location using Desktop Web. It's still flaky trying to set location from Mobile Web.

9 months. No change.