Hi Doodle,
Assuming you are in the UK? If it's the Dogs Trust then you are OK, but not the RSPCA as they unfortunately don't have a good track record (though there are some lovely individuals working for them). Many Tears, sadly, are also not no-kill.
Is it a pound or a rescue? Pounds usually house strays on behalf of local authorities and after seven days they can be killed. Most (not all thankfully) therefore wouldn't be no-kill.
Most no kill rescues are happy to say so on their websites - this doesn't mean that a dog in their care is never PTS - but the circumstances will be very tightly defined e.g. severe illness etc.
If the rescue is a properly structured charity then a great deal of their information including income, outgoings etc will be on the Charity Commission website. If I was looking for a job, I'd want to look at this since I'd want to know they were going to be financially stable to pay my wages! 
You can also have a look at the Rescue Review Website - see if your rescue has any writeups on there?
Alternatively, if you'd like to name them, then i'm sure lots of peeps on here would have info on them. If you don't want to name them publicly, PM me - I have lots of rescue contacts around the country and am still in touch with Valhalla - between us, we prob know most!
Lastly, it is possible that they may be inspected/licensed by the local authority, and if they are, then you are entitled to see any inspection reports. Also worth asking if they are members of the Association of Cats and Dogs Homes - kind of a trade body - most of the big rescues are members. Again, non membership isn't a negative, but membership to me indicates that they are willing to learn and exchange best practice, which is usually a good sign.
Also, there are the annual Burgess Wetnose Animal Rescue Awards - these are awarded annually and I know several charities who've won - again, usually a sign of a good operation.