What size wire and conduit do I need to run to a subpanel in a garage?
If you plan on replacing the 50 Amp breaker with a 100 Amp...

The minimum sized conductor is #3 THHN copper which includes the 2 hot legs and one neutral.
The minimum sized grounding conductor is #8 THHN insulated copper.
The minimum sized grounding electrode conductor (for ground rod) is #8 bare copper.
The minimum size conduit would be 1 1/2&quot; using PVC schedule 80.

If you plan on keeping the 50 Amp breaker...

The minimum sized conductor is #8 THHN copper which includes the 2 hot legs and one neutral.
The minimum sized grounding conductor is #10 THHN insulated copper.
The minimum sized grounding electrode conductor (for ground rod) is #8 bare copper.
The minimum size conduit would be 1&quot; using PVC schedule 80.

Notes

The above figures are based on a detached garage @ 100' or less distanced from the garage to the houses main panel. An additional ground rod is required for detached garages.  If the garage is not detached then an additional ground rod is not required.
If detached, the subpanel would require its own main breaker and the grounds and neutrals would need to be separated. Otherwise a main lug subpanel is fine but still need to separate the grounds from the neutrals.
The above examples are based off the National Electrical Code 2014.  Your jurisdiction may have other requirements.

References

Table 310.15(B)(16) Allowable Ampacities of Insulated Conductors.
Table 250.122 Minimum Sized Equipment Grounding Conductor.
Table 250.102 (C)(1) Main Bonding Jumper
Table C9 Conduit fill.