Magadi lake, south of Nairobi

Hire a Suzuki and drive there yourself.

thanks for the "illuminating" replay.
any chance someone else could tell me if there is public transport going there, that i am not aware off?

Hehe...
You've beaten me to the draw just now...

You could try to first get there and use the local transport network (known as matatu "Mar-tar-too"). It is more than likely that they will be plying the route.

Having said that, there is absolutely nothing exciting about Magadi; the entire town simply comprises the "premises" of the Magadi Soda Company, and the lake has been "cultivated" to meet their requirements.

Getting to Magadi is easy. Matatus # 111 and 126 leave constantly from the train station and go to Kiserian (70 KSh) From Kiserian, there's only one other matatu route, and it goes to Magadi (it waits on the main road, beneath the electrical transformer) for 250 KSh.
That can get you from NBO to Magadi in just under 2 hours. If you don't plan on spending the night, ask when the last matatu runs.
The big problem now is getting around town. There is no public transport in town, but you might be able to find someone with a car or truck to drive you for an hour.

Another, much more memorable alternative is to ask around in town for someone to stay with for a night or two, preferrably out in one of the bomas/manyattas. This means walking down along the lake for an hour or two and sleeping in a mud hut in a maasai village, with only a spiky bush fence keeping the hyenas out.

As far as the whole lake being "cultivated" and/or lacking natural beauty, I think anyone who's seen The Constant Gardener would disagree.

Bring water.