A stealth aircraft isn't actually invisible to radar. It's just harder for current radars to see stealthy aircraft at longer distances. This gives a stealthy aircraft the element of surprise against an enemy. So at a long-range a stealthy aircraft radar signature will be a lot smaller than a regular one perhaps the size of a small bird which will get ignored.
However, a small bird flying at Mach one will probably give the game away, lol.
It's always been the case with military attack aircraft in that he who shoots first, usually wins.
Non-stealthy aircraft can employ other techniques to be stealthy or hidden such as low-level flying whereby the ground will obscure you until your close enough as aircraft will be obscured by ground clutter to a scanning radar. Also the curvature of the Earth can obscure you if you fly low enough, you can get as close as 25nm or so before being spotted. Anti-ship missiles employ this technique.
But in open air/space a stealthy aircraft will be picked up a lot later than a non-stealthy one flying toward an enemy monitoring in that direction.
This does not apply to any visual systems as a big hunk of metal in the sky is just as visible. Also, heat-seeking (infra-red) systems are less affected as heat is heat, and all you can do there is try and mask your heat signature. But these tend to be shorter-range systems.
To answer the question. Friendlies have the exact same problem as the enemy, as they don't have any special radars that can see a stealthy aircraft any better than the enemy can, that is unless you know what you're looking for/listening to.
Security aside the stealthy aircraft will by some means broadcast its location on a random occurrence and securely encoded radio frequency, so as long as you know what to listen for and how to decode it you can work out where your assets are. Obviously, the enemy a) won't know what to listen for and b) know how to decode it.
These details are set on an aircraft pre-flight much like IFF/SSR transponder codes and for obvious reasons are very very secret.
Radars are essentially passive so this limits their range, however, if something is broadcasting the detecting range is increased.
(Simplified example) Think of it as looking for something in the dark (or very low light). Without illumination, you can't see anything until it's up close, but if that thing turns a light on or otherwise illuminates itself then you can see it.
Now if the thing is illuminated all the time everyone can see it which isn't a good idea. So imagine then the light is a certain colour and only you (and the thing) know what colour to expect. Turn the light on for a short time and you can see it as you are looking for it, but its not on long enough for anyone else to figure out there is a light on let alone workout what colour it is. Get the idea :)