Observing ethernet auto-negotiation packets using oscilloscope
You need:
A scope with (most likely) 500Mhz bandwidth and 1 Gigasamples/s
A differential probe with (most likely) 500Mhz bandwidth
(You could go lower on the speed if you only want to look at 10Mpbs, size your probes appropriately to be faster than the speed you want to look at)


Source: http://www.learnabhi.com/ethernet-cable-categories-cat1-cat2-cat3-cat4-cat5-cat5e-cat6-cat7-cat8/

Then you wire up the orange pairs like this, and 

Source: Tektronix vid with annotations

After that you can set the trigger level and decode it by hand. If you want to pay more some of the newer scopes have software features to automatically decode Ethernet packets (like an MDO3000). 

A logic analyzer might work (I have not tried this) if it had a differential probe, all the logic analyzers I know of have a 0V to 30V span (or some upper limit) which would make it hard to detect the differential signalling of Ethernet.