There is plenty of room for good two word domains, and will be for a long time to come. There's still a lot of one-word names available too; many of them sound stupid in isolation but it's the product which makes the name in the end. A good name should be easy to remember and repeat to another person, and you achieve that by stimulating an emotional response. If it's also functional/descriptive that is a bonus, but not necessary. You should also allocate some time for doing trademark searches etc. You must go through a lot of names and be patient.
I intensely dislike the current wave of domains like 'weeb.ly' 'grobble.com' 'nu-spella.com'. Most of them feel so forced and fake, like in bad science-fiction movies for kids. Unless kids are your target market, don't ask them for suggestions. You can use a completely made up name (such as anigbrowl) if it feels right, but some feel natural and some feel forced. This often seems to mirror the quality of the product, but maybe I'm just telling myself that.
There are many other techniques - dictionaries, letter shuffling, and so on. In fact there are specialist naming companies that will put together hundreds of names and spend hours discussing them, checking against trademark registries etc. Corporations use them all the time. One firm I know will charge a tiny startup $5,000 but they'll make a big corporate client sign up for $250,000. Of course that includes focus groups, international trademark clearances, checking a name doesn't mean something embarrassing in a foreign language etc.
whois whatever.com
Brainstorm, repeat :)