4 days is pushing it. To have a successful crack at it, you should really aim for at least 5-6 days, allowing for travel time to get there.
If you want to do it cheap, I guess the Naro Moru route would be the one as its the most popular. However I would recommend the Chogoria route as its very beautiful. This is the route I took, and then you can descend via the Naro Moru route, thus getting to see the mountain from two routes. First, you have to get to Chogoria village. Find yourself a guide (and a porter if you can afford it). You can't enter the park on your own, so a guide is essential.
From the village, you then have to get to the park gate - you'll have to hire a jeep or hitch a lift. Or walk the 30km. At the park gate, there are some fantastic bandas, but if you're on the cheap, you'll have to camp. I highly recommend you stay 2 nights here, because your body will need to acclimatise (the gate is at 10,000ft). However, this is a personal thing - some people acclimatise better than others. Having failed twice on Kilimanjaro

because of this, I know from my own experience that it pays to spend more than one night at these heights...
From the gate to Point Lenana, its two days, and then its possible to get all the way down to the Naro Moru gate in another day. From here you can find transport back to Nairobi.