If your only complaint is trading fees, ask your current broker if they can reduce the fee. If that doesn't work out, transfer your account.
Find a new broker, open an account, and ask them how to transfer your account. Most brokerage firms participate in the ACAT System (Automated Customer Account Transfer System) which transfers your account assets in about 5-7 business days and takes care of any trailing income (e.g. you're owed a dividend payment but it won't credit your account for another month -- transfer your account now, and next month when the dividend credits your old account, ACATS pushes the money over to your new account.) Most ACATS-participating firms will also transfer your cost basis information along with your stock.
The downside is there may be a fee for ACATS transfer charged by the broker you're leaving. Could be small, could be $100.00. If your account is simple (like, 1 or 2 stock positions,) it's worth it to avoid the ACATS fee by opening the account at your new broker and then asking your old broker to transfer each stock to your new broker via DTC free delivery ("free" in the sense of broker A is sending stock to broker B without expecting payment in return. Some brokerage firms charge for free delivery but it's usually less than ACATS.) However, any follow-up for trailing income, closing the old account, and tracking cost basis then becomes your responsibility.