1.
groping, feeling one's way
Physically reaching out and touching to find something in the dark or without being able to see.
2.
trial and error, fumbling, feeling one's way
Proceeding cautiously without a clear plan, figuring things out as you go.
Writing
手 (hand) + 探り (searching). Literally "searching by hand."
Usage
Often used adverbially with で: 手探りで (by groping / through trial and error). The figurative sense (sense 2) is very common in business and project management contexts to describe proceeding without a clear roadmap.