I'll pre-empt those that are going to say "Learn programming" or other "Learn another skill" posts. Other people have said that "Everyone can be a designer, not everyone can be a programmer" - this is something I highly disagree with, but for the purposes of this discussion - let's assume that it's true and I, and by proxy, other people, don't have the requirements to be something else.
When recruiting artists or programmers, you look for examples of previous work. This would work for a designer too obviously, and if the protential recruit has previously worked on a game in his role, then he can show off what he's done. The problem is with people looking to start in on their first game.
A programmer who hasn't worked on a game before can usually show work of other code he has done from a non-gaming perspective. The same can be said of artists. A game designer won't have this possibility - or not as a demonstrable item. There is documentation that he could produce (GDDs, High Concepts) but their worth is questionable without a finished game to accompany them, or at least some sort of prototype.
The question is therefore, how does a Game Designer prove his worth?
My initial thought is to produce the documentation I mentioned previously. A concept, high concept, Game Design Document (GDD) - whatever you can. I've heard it said that a GDD is worthless without a prototype or a finished game. This may be true from the standpoint of judging the worth of the game, but not in judging the worth of the designer. If the designer can produce polished, high quality, concept documents and such, then you know that he can do at least that. It is something that a Game Designer must be able to do from a professional standpoint, so having some to judge is a definite must.
If you produce documentation as a proof, produce several documents for different genres. If you produce 5 highly polished design documents for 5 well thought out RPGs, then it could be very good - assuming that whoever is going to look at them is interested in RPGs. However, if they want to make something different, then you're giving the impression that you are not suited to the task. Making design documents for widely varied game types - like designing a serious gruesome horror FPS, a sci-fi RTS, and a cute and fluffy casual sim game - shows that you have the ability to work with whatever genre is required whether you've implicitly designed in that genre before.
Beyond this, I am at an empasse.
Level designing for an existing game has been suggested to me. This is something I have obviously dabbled with, mostly with RTSs (Age of Empires II, Red Alert 2 & 3, Empire Earth) and some FPSs (Halo 3 / Reach) but to what degree is it worth pursuing? Game levels in various editors are relatively simple to produce, but I have trouble seeing their value without rigourous play-testing.
If I produce a dozen maps for various games, am I to leave it to the recruitee to judge if they're any good?
Do I need to host them online and get others to play them for me in the hopes of gaining some sort of feedback?
What of maps which do not score as high as anticipated, should I show different iterations and re-designs which lead to more enjoyable gameplay?
What else could I (or another designer) do in order to show off their ability without the option of producing a game by themselves?
Inevitably there will be people that suggest that I stop trying to be "the ideas guy." I am not looking for a cheap path to be carried by a team and provide nothing of any worth. I want to be a Game Designer, not an Ideas Guy. They are not synonomous. A good game designer adds value to the team, and I want to put myself in that position. You may believe that the others in your team can design your game without a dedicated designer - this could be true, and I wish you luck - this doesn't mean you should assume that all designers are just slackers, because we are not.