You can only focus on one profession at a time, and must have proficiency in a certain tool or language in order to access a profession. Following that, you must complete a trial set by the DM, usually during downtime. This might come in the form of a number of ability checks related to the profession as well as an event, such as winning a local, national, or even international competition, creating a masterpiece, or another meaningful trial as set by the DM. These trials can often include a monetary expense, and after successfully completing the trial you unlock the next tier, while on a failure you must reattempt the trial at a later date.
Benefits from professions are split into the following tiers; apprentice, journeyman, master, and grandmaster. In order to unlock the next tier, you must have all of the previous tiers unlocked. The tiers roughly correspond to level ranges; apprentice to levels 1-4, journeyman to levels 5-10, master to levels 11-16, and grandmaster to levels 17-20. Characters should be able to attempt trials within those tiers, though depending on the campaign, this may not always be the case.
If you would like to change your profession, you may do so at any time. However, whenever you unlock a new tier within a profession, if you already have a total of four tiers unlocked from all of your professions you must choose to one of the benefits from any tier within a previously chosen profession (though not necessarily of the highest tier you've unlocked). You lose all benefits from the chosen tier, which reflects the focus on the new profession and old skills falling to the wayside.