Things that you can do now (i.e. pre-medical school) assuming you have a job:
1. Invest in tax-advantaged retirement accounts (always check contribution limits with the IRS yearly)
- Roth IRA: Invest up to $5000 of post-tax income per year (subject to income limits, none of which you'll probably meet before being a doctor). Growth and earnings are tax-free(!). Tax-free growth over 40 years is pretty awesome.
- 401k: Invest up to $16500 of pre-tax income per year (subject to income limits), income taxes are deferred until withdrawal of funds. Reduces your federally taxable income (ex. $50000 gross income - $10000 contribution to 401k = $40000 of taxable income). Many large employers have a match program; if yours has this, do it if at all possible. It is free money! (ex. 1:1 match up to 3% of income; you contribute 10% of your income, employer adds in another 3% = you added 13% of your income this year).
2. Invest reasonably but conservatively. Since you're young, you should be taking more risk (i.e. stocks v. bonds) but don't mess around with investing in individual stocks. Unless you are extremely good or lucky, you won't beat an index fund or another type of fund the financial professionals arrange. If you are that good, you should consider going into finance instead of medicine. Choose funds with low expense ratios.
3. Have luck. This can't be engineered, but if you're lucky enough to invest at a local low and things go up, you're golden. Otherwise, just sit tight. Investing for retirement is a long plan, so if the market tanks in the short term, don't worry and sit tight. It will go back up and you don't want to be the person who lost a ton of money by fleeing at a low.
4. Remember, finances that are in federally-defined retirement accounts are not counted into usable assets for paying med school tuition by most medical schools. Therefore, you can have a pool of money growing over the 7+ years of training that isn't going into tuition. It may be a minor way to offset some of that massive opportunity cost.