After completing training, in all fields there will be a written test to obtain board certification. A very few fields still require an oral exam as well. This test is typically a one or two day event and may have a passing rate of 50-90% depending on the field.
Those who (sub)specialize may also be required to take a certifying examination after they complete their specialty (fellowship) training.
After that, most, if not all, fields now only give time-limited certification. That means you have to recertify periodically, usually every 7 years, but there may be some variation in that. The processes for recertification are highly variable among fields, but generally require a proctored written exam AND some evidence of continuing education and various forms of demonstration that you are actually doing medical practice. These guidelines are still evolving in many fields. You can look up the American Board of Internal Medicine, American Board of Pediatrics, etc to get more info.
The process of certification and recertification is a big part of post-residency life. You are not done with being tested when you finish medical school.