Does your company match 401(k) contributions? If they don't, and the plan choices have high expense ratios, an IRA may be a better place to start. But yes, once you've contributed the annual limit, your company automatically stops further contributions (which will make your paycheck deposits get bigger).
An IRA has nothing to do with your company, except that you must have an income to contribute. You contact a company like Vanguard, Schwab or Fidelity to setup an IRA. You'll fill out an account form and send them a deposit. An IRA is an account type: you will still have to pick what to invest in, inside the IRA.