The answer to this question depends on what kind of veterinarian you are referring to... small animal general practice, small animal specialty practice, equine general/mobile practice, equine surgical practice, dairy/beef practice, poultry, public health, zoo vet, wildlife vet, professor or researcher.
As someone who has practice in small animal general practice and specialty practice I can give you my perspective.
Many general practitioners work 4-5 days a week. Your day starts at 8am or 9am. You may start seeing clients and patients (people an their animals) in the morning. During the appointment that will last 20-30 min you will talk to the owner about their pet's health concerns and perform a physical exam on the animal. You would then order tests like blood work and x-rays that you technician are likely to perform. You may then have to discuss the results of some tests with the pet owner, and prescribe a treatment, which may be medications, or may be a procedure like surgery. In the afternoon, you may have some procedures like dental cleanings, and surgeries (spays and neuters). At the end of the day you would have to discharge the patient's who had procedures done, you may need to call and talk to owner asking for up dates on the patient's, giving the clients the result of test that were sent out to the lab (like blood work and fecal analysis). At the end of the day and through out the day you will need to keep good records: recording conversations you had with the clients, your physical exam findings, any interpretations of tests you performed, and any treatments you have prescribed. And your day may will end at 6 pm or 7pm, but in realistically, your done when all the work is done.
As a small animal specialist, the day look mostly the same, but depending on the specialty you may spend more time performing certain procedures. If you are a surgeon, you may have one day when to see clients and patient and one day when you spend all day in the operating room performing surgeries. Or if you are a radiologist, you would spend very little time talking to client or having hands on contact with patients, but spend most of your day reviewing radiographs (aka x-rays), CT and MRI scan, writing reports, and consulting with other veterinarians.
Now if you ask a vet who works with horses, cows or chickens, their day may be different. A vet who works for the government inspecting animals and animal products for import and export, they will have a different day. I think regardless of the type of vet you are, you must be a good communicator, be able to write well to keep thorough records, think of things critically, but also be able to improvise, and be patient and caring for both people and animals.