How are antennas integrated into stealth aircraft?
Pitot tubes
F-117 pitot tubes

Source: YouTube. Also a look at the FLIR and DLIR.
F-22 pitot tubes

Source: AIR-SCENE UK.

Incorporation of those pitot probes were a cost savings measure. They are also a dominant RCS signature source in the forward and side sectors. The original ATF proposal was for a flush air data system that would have cost many $ millions. - djcross, F-16.net

F-35 pitot tubes

Breaking Defense. More pics on F-16.net.
Canopies
The canopy keeps radar energy out of the cockpit, the inside of which is filled with messy odds and ends. The F-22 and F-35 canopies are gold-impregnated for this reason. Note: the F-22's canopy is possibly doped with indium-tin-oxide, not gold.
In the EA-6B's case, the gold keeps the a/c's own radar energy out of the cockpit---those ram-air turbines are powering two jamming pods. The coating (and a similar one applied to visors) also turn black to protect the pilot's vision from nuclear detonations.

Source: USAF

Source: Wikipedia.

Source: Lockheed Martin. Flickr set.
Notice the similarly tinted/treated window beneath the F-35's nose. That's the aperture for the EOTS (electro-optical targeting system), an IRST and ground targeting system. Also note the two small pitot tubes above the EOTS. I remember pitot plates were being developed for the F-35 (which are stealthier but more difficult to develop), but I haven't heard anything about it in a while.
Sensor apertures
The coverings are transparent to the operating bands of the radar/radio/etc underneath.
The F-22 and F-35 have fixed AESA radars. The latter is angled up to minimize returns.

Credit: Northrop Grumman. Hi res.
Some radar energy enters through the aperture. Whatever isn't reflected is absorbed by the radar itself or heaps of RAM, which hides the messy rear/sides.

via F-16.net. More AESA pics.

Fun note, the first F-35 radar pic is of an APG-81 installed on the CATBIRD:

Source: YouTube

Did the F-117 have a radar warning receiver?
It's always been a contentious point. Some say yes, some say no, some say 'I like my job.' In a lengthy 2007 interview, Lt. Col. Dale Zelko (the F-117 pilot shot down) declined to reveal whether the RWR (if any) warned him of the missile launch, citing sensitivity. He only reconfirms that he visually tracked the missiles. My guess is the F-117 may have a limited radar warning capability, but perhaps not in the relevant band. If he or the mission planners had detected and thus been aware of of the radar sites, you'd expect them to plan better routes to avoid the threats.
I leave you with a quote from Maj. Gen. Carlsons' (who flew the F-117) briefing on stealth fighters in 1999, shortly after an F-117 was shot down in Allied Force.

We started out a long time ago building airplanes that had low observable technology incorporated into their design. The SR-71 was an example of where we took the aerodynamic design and then added some radar absorbing material to the airplane to make it slightly stealthy. And I'll give you a representation of that graphically here in a minute. We went to the second generation of airplanes and you can see we designed that airplane, the F-117, essentially from the bottom up to be stealthy. It was crude technology. It was developed at a time when we didn't have the modeling and computer power we needed to make the kind of aerodynamic design that we would have liked, but we built one that we thought was very stealthy. And of course, the night that Desert Storm opened the quote from Col. Al Whitley still is famous in the Air Force: &quot;Boy, I hope this stuff really works.&quot; And of course, you know that it did. That isn't exactly what he said.
Then we came to the third generation of stealth airplanes. We built the B-2. And of course, by that time, we had the modeling tools and the design tools and the computing power to make an aerodynamic design that was optimum. And this airplane is [a] much higher altitude, much better performing airplane than the F-117. We were able to eliminate a lot of the radar absorbing material from the structure. And by the time we got to the fourth generation, we were able to add supersonic speed, the agility of an F-15, F-16 class airplane and do that with no degradation to the stealth. In addition to that, we were able to add a number of apertures, in other words, openings in the airplane's surface for antennas, radars and other sensors. And in the F-22, as an example, there are over a hundred of those apertures on the airplane, where if we jump back a couple of generations to the F-117, there are essentially a couple of aperture openings and the rest of them we hide when we go into combat. [Emphasis mine.]

Some of the F-22's apertures...


Source
...whose functionalities were consolidated in the F-35's fewer apertures (some shown here).

The F-35's ASQ-239 EW suite, an evolution of the F-22's ALR-94, consolidates 30 senors down to 10.

[Apologies, pressed for time. This answer will be brief, unlike my previous 29,999 character response.]