This can be quite a project but if you are willing to put in the time and effort (and work on your salesperson skills), you should eventually be able to connect.  Here are some thoughts:

• If first time, it is probably best to start with a letter or an e-mail.
• If you have already met (in-person or over the phone), make sure you have something meaningful to say.
• Even if you have some great news to report (i.e., you earned straight As or won moot court), consider writing a letter.
• If using the phone, consider whether you really need to speak to the partner or whether you can accomplish your goal (future in-person meeting or phone date) by speaking with the assistant.
• Befriend the partner’s assistant — the most important person standing between you and the partner.
• Strike a balance between being pushy and annoying but yet firm and clear in your desire to speak/meet directly with the partner.
• Do not leave voicemails which depends on the other person taking action. 
• Ask the assistant the best way/times to connect with the partner. 
• Stress that you only need five or so minutes of time.
• Be very flexible — you can come in whenever convenient and are willing to wait.
• Watch tone, use words carefully, and get right to the point (the assistant’s time is limited too).
• Do not take anything personal.  Perhaps the assistant is short with you or even rude because he or she does not like you or is having a bad day.  Not your concern.  Your goal is to get that person to like you and help you.

Good luck!  Feel free to post your results or share your experiences.