We study the production and detection of the standard-model Higgs boso
n at the Fermilab Tevatron. The most promising mode is WH and ZH assoc
iated production followed by leptonic decay of the weak vector bosons
and H --> b (b) over bar. It may be possible to detect a Higgs boson o
f mass m(H) = 60-80 GeV with 1000 pb(-1) of integrated luminosity. We
also study the signature for a nonstandard ''bosonic'' Higgs boson who
se dominant decay is to two photons. A signal is easily established wi
th 100 pb(-1) in the WH and ZH channels, with the weak vector bosons d
ecaying leptonically or hadronically, up to m(H) = 100 GeV.