The component specs may indicate Propagation Delay, Tp, for each polarity. Sometimes this is called Latency when measured in faster clock cycle delays. It is measured at the Logic Family threshold voltage for input and output. ( e.g. 1.3V for TTL and Vcc/2 for HCMOS )
First you want to make sure your test method uses calibrated probes using the square wave test waveform to give zero overshoot. There is a trim cap on 10:1 probes.
Second you want to ensure that your probes are low inductance, which means your grounds must be common connection , short in length and have flat braid wire or a ground plane. Your ground clip wire must be very short ( a few cm) for sub microsecond or ns measurements, if not then remove the clip and have two pins with signal and ground near the chip and use the pin centre and barrel ground for best signal capture. ( Tektronix has a spring barrel adapter to make short measurements between tip and gnd ring. )
Third, you want to calibrate your probe by measure the tip on your ground to make sure it is flat line with no common mode noise. It may be that you have a lot of AC hum on your ground from inductance or stray noise spikes.
Fourth and most important , you want your trigger source on the scope to be broadband ( not filtered )and DC coupled for stable trigger threshold. AC coupling and noise reject are useful too but if you have a clean signal, then trigger should be reliable. DC trigger should give stable pulses, unless the pulse has AC common mode hum wandering up and down.
If you can not trigger reliable square wave using the front panel test signal pin on the scope, then there is a fault with the scope setup as above ( e.g. missing ground connection or ground clip wire too long) or a problem with the scope.
Then you can get textbook looking waveforms.