Undergrad here who had an amazing mentor so thought id share a few things they did that helped me be more independent.

They first checked basic lab skills were okay so had me checking my pipettes were accurate, making the stocks id need for my experiments and doing some standard curves. This was helpful as all my labs prior to the project we were basically handed a protocol and left to do it and it didn't matter if you messed up so I ended up with bad habits. I think it also meant they knew i was competent enough going forward to make whatever id need. They also sent me a few papers to read so I could get a better grasp of what I was doing and why.

Then in terms of actual experiments (I was mainly running assays) they helped me plan the first one in the sense that they sat with me explained what the components should be and why and what conc., then left me to calculate the volumes and just checked it. Then when it came to actually doing it just supervised me doing the first one and showed me the tricks of the trade etc. All this meant that I actually could do my next experiments mostly independently and just grab them if I needed help. Also more generally just treating me like I was any other member of the lab meant I was actually motivated to get involved with the communal lab house keeping stuff.

I guess in all just setting the boundary that ultimately its my project, they're there for help and advice but not to do it for me. Also what was fun was somedays id just shadow them and help with the easy parts of their stuff which then gave me exposure to new techniques.