What are the advantages and disadvantages to leasing a new car as
opposed to buying the car and how do I decide which option is the best
for my personal financial situation?

Assuming that you would finance the car for the same period of time as
the length of the lease, the main thing to focus on would be the
monthly payments of each. Compare the two and choose whichever is
less. But remember, at the end of the loan you own the car, so make
sure to factor that into your decision. Also, in a lease the car
dealer will charge you an exorbitant per mile fee if you go over the
usually low mileage limit. Make sure you factor all the costs
associated with a loan and a lease into your decision. Hope this hels
you make your choice!

In almost every case, buying and keeping the car 8+ years is the
better way to go.  The total cost of owning a car 8 years is
considerably less than owning (or leasing) 2 cars of the similar value
for 4 years each.  With that said, there are circumstances when you
will only want a car for 3 or 4 years:
-If you are fairly certain you will move far away at that time and
will not be taking your car with you.
-If you know you will be making much more money in the future and only
want a cheap car for several years.

Advantages of leasing:
-Slightly cheaper during the actual years of leasing
-You have a fairly new car all the time so maintenance/repair costs
are low and the car is more reliable

Disadvantages of leasing:
-You pay considerably more in the long run in car expenses (needing to
lease 2 or 3 cars instead of buying 1)
-Insurance on an owned car is often cheaper than on a leased car (also
along these lines, insurance on an older car is cheaper... and if you
own the car longer it will be older)
-Leases often come with mileage restrictions and you pay alot if you
exceed them (and get less than you paid for if you don't meet them)
-Any damage to the car will often cost you more in a leased vehicle
than in one that you own  (the dealership needs the car to be like-new
to sell it when you are done leasing it)

I recommend that you look at the total cost of leasing the car:
-Down payment
-monthly lease
-call the insurance company and ask for 2 quotes... lease vs buy
-extra mileage costs if you think you might go over

Compare the costs of leasing vs buying for 4 years & 8 years and
remember to include the value of the car that you would own.  In 4
years, the total cost will probably be very similar... but in 8 years
(considering you must have 2 leases during that time), I'm certain
that buying will be much cheaper.

Generally, buying is better for the reasons already cited.

However, for business users, there MAY possibly be some tax advantages
in going the leasing route.

Otherwsie, I would avoid leasing LIKE THE PLAGUE.

Yes, even if that means wearing a Plague Mask.