If you go to your data sheet, and look at p. 3, you'll see a section called ON Characteristics, and there is a field for Vce(sat). It gives 2 examples, in both cases with a collector/base current ratio of 10. Likewise, figures 2 and 3 show saturation characteristics, and in both cases the upper left part of the figure specifies a beta of 10. Beta is also called hfe, and is (roughly) the ratio of collector to base current.
You can find a quick description of what transistor saturation means here http://en.wikipedia.org/wiki/Bipolar_junction_transistor. There is no hard-and-fast rule concerning the current levels which will mark the transition from active to saturation, (it varies with collector current and the transistor) but the rule of thumb is that a beta of 10 will always get you there. In fact, a beta of 10 will generally get you into hard saturation, where small changes in base current will produce small changes in Vce.
So the more detailed answer to your question, taking into account your supplementary information is this - First, calculate how much current you need to drive: for a TTL circuit, you need 1.6 mA per gate, or if you're looking at a resistor pulled up to 5 volts it's obviously about 5/R. You pretty much can't go wrong with a base drive 1/10 your specified load current. In your case, a 9 mA base drive will do the trick. You can do this in TTL by providing a pullup resistor of about 300 ohms and a base drive resistor of about 200 ohms, and this is (just) within the output capabilities of TTL. Note that, from figure 2 of the data sheet, this will typically produce a saturation voltage of ~0.15 volts. If you can live with a slightly higher output voltage you can provide slightly less base drive, and extrapolating from the data sheet (always dangerous) your worst-case output voltage with a 9 mA / 90 mA combination ought to be under 0.4 volts.