  The appearance of high energy tau neutrinos due to $\nu_\mu \to \nu_\tau$
oscillations of extragalactic neutrinos can be observed by measuring the
neutrino induced upward hadronic and electromagnetic showers and upward muons.
We evaluate quantitatively the tau neutrino regeneration in the Earth for a
variety of extragalactic neutrino fluxes. Charged-current interactions of the
upward tau neutrinos below and in the detector, and the subsequent tau decay
create muons or hadronic and electromagnetic showers. The background for these
events are muon neutrino and electron neutrino charged-current and
neutral-current interactions, where in addition to extragalactic neutrinos, we
consider atmospheric neutrinos. We find significant signal to background ratios
for the hadronic/electromagnetic showers with energies above 10 TeV to 100 TeV
initiated by the extragalactic neutrinos. We show that the tau neutrinos from
point sources also have the potential for discovery above a 1 TeV threshold. A
kilometer-size neutrino telescope has a very good chance of detecting the
appearance of tau neutrinos when both muon and hadronic/electromagnetic showers
are detected.
