As mmckenna noted, one will typically end up on foot during the search, so you're reasonably set with your dual band directional antenna and a receiver/transceiver with a reasonable signal level meter. One that displays RSSI is great. Attenuation definitely comes into use and turning your back to the signal with a directional antenna in front helps to also narrow the direction when you get close. Remember 360° turns are prudent. Also, do not forget harmonics. Your dual band antenna will come in handy if you're looking for 146.565 and dial up 439.695 when the signal becomes stronger. This is very handy when the radio will not attenuate further and you don't have an inline attenuator to add. Additionally, if the signal appears to be using a vertical antenna, turning your directional antenna horizontal may add up to 20 dB of attenuation for a quick and easy option.
As to equipment, I use an Icom R30 which offers adjustable attenuation. I use the dual band Elk Log periodic for the directional antenna. While I have stuck with the Elk, I have used much lower cost receivers over the years.
Good equipment helps, but trial and error from practice is the best investment.
What kind of equipment would you recommend for signal finding in the VHF and UHF Bands?
I currently rely mostly on signal strength and a directional antenna, but i'm sure there's better ways. Any advice?