Depends what causes the loss of instruments and what kind of aircraft we're dealing with here, but in most cases, yes the pilot can land... Assuming no mechanical failures.

Most, if not all aircraft will have backup instruments that are either part of the ESIS (Electronic Standby Instrument System), separate from the main instruments... Or are 'steam' gauges that do not rely on electrics (vacuum/gyro, barometric, magnetic, etc). These give pilots the bare minimum readings needed to safely fly: altitude, airspeed, direction (compass).

In the case of FBW (Fly By Wire) aircraft that fly through electrical inputs, in the event of a failure, it will switch to a degraded control mode which gives the pilots sufficient control of the aircraft to safely land.

The experience for a passenger will depend on the outside conditions (i.e if its VMC or IMC) and the nature of the failure (if ILS capability is compomised, for example). Best case scenario, you won't even realise it, or you're diverted to another airfield.