How To Approach Small PE Firms

I’m a rising sophomore at a non target, and I am looking to get any experience I can this summer relating to IB, PE, etc. I’m currently in an internship where I work on some Excel models for the operations and finances of a small business, but I know I could supplement this summer experience with some apprenticeship or shadowing.

I live in a medium sized city in South Fl, and I’ve identified a couple relatively small PE/VC firms decently close by. I noticed some even have alum from my university.

I’m becoming more proficient in Excel and have been studying some behavioral and technical questions, but even with that learning I’m curious what I could provide the firm and how I can reach out to the firm for possible shadowing/apprenticeship.

**Also, I understand that I should’ve done this earlier in the summer.

Essentially, my question is: If you worked at one of these smaller firms, how would you want a younger person to approach you (given I can provide 0 value - unless for running to go get coffee or something).