Educate Yourself
There are thousands of books and periodicals explaining securities, markets, and in inner workings of stockbrokers and investment firms. The more you learn, the sounder your decisions will be.
Keep Neat, Orderly Files
Even small accounts generate a lot of paper. If a problem should develop, the burden is going to be upon you to establish what happened and when it happened, and who said what or failed to say what. Should mediation or arbitration become necessary, you will need to make all that clear to a lawyer and expert witnesses so your case can be effectively presented.
The side with the best records usually wins.
Check Everything Sent You
Your investment firm will send you a confirmation statement (notice of the trade, including date, price, etc.) and monthly account statements. Check them carefully for mistakes and irregularities. If something is amiss, call the broker, and if that doesn't bring satisfaction, call the broker's supervisor. Investment firms are large, busy places.
Mistakes happen. It is always easiest to correct a mistake while it is fresh.
Complain in Writing
If a problem is not resolved to your satisfaction, send the firm (not the broker) a letter with copies of all relevant documents. Be clear and precise. The things for which stockbrokers and investment firms are accountable are discussed above under the heading "FRAUD AND NEGLIGENCE BY STOCKBORKERS AND INVESTMENT FIRMS". Explain why your complaint fits into one or more of those categories.