I might be able to help some since I used to sell cars, but ironically I've never leased or financed a vehicle. I always buy junk and fix it up
Financing is simply a loan where the car itself is collateral. The bank holds the title and you make payments to the loan. When the loan is paid off, they give you your title. It is equivalent to buying a house. You get a loan where the house is the collateral and pay it off a month at a time
Leasing is like a long term renting an apartment. The dealer holds the title, you pay into the account. You are basically paying for the depreciation you are causing the car. It works out to be more than the actual depreciation, but its basically a rental. At the end of the lease term you have a couple options. If you've stayed within the mileage and wear limits, you can surrender the car and stop payments. Unlike an apartment, leases also have a guaranteed buy price at the end of the term. If you lease a new car that costs $30k for 36 months, they decide on an end-buyout price when you buy it; say $20k. After the three years, you have the option of buying it for the pre-arranged price. A lease can sorta be summed up as financing that only lasts for the length of the term and you have no equity in the car.
Each buyer is different. Credit scores, amount of down payment, trade, and income all play huge roles. For each person, the best method is dependent on all of these factors. Myself, for instance... I have no credit. The credit I do have is OK, but my income is steady. I am probably wisest to save my pennies and buy with cash. I could get a loan, but my interest rate would be very high.
Leasing is a good option for some beginners. It takes less credit and often less down payment to lease. The benefit is that you can make payments on a car which boosts your credit. Then, three years (or however long the lease is) later you have the option to buy the same car at 2/3 its original value with better credit.
Take a look at all the numbers and add them up. Financing can be a six year obligation, but with today's rates it may actually save you money. If you liquidated $30k worth of stock to pay cash for a vehicle, you have to look at what interest income you've lost over the next 6 years. My guess is that its more than the 3% you would be paying on a car loan. Or if you have $30k cash from the lottery, it might be wisest to invest that $30k and get a low-interest loan for the car. You might make 6% on the investment and only spend 3% on the loan. If you just spend the cash on a car, its just gone. The car company invests it and makes 6%
A lease is sometimes the only option, but its rarely the wisest. Look hard at the deal. If you decide to lease then surrender, you've just spent money that doesn't come back since you have no equity in the car. If you decide to lease then buy, you've just paid $9600 into a lease contract and you're going to end up paying another $20k on a used car. Leases are also usually pretty restrictive in mileage allowances and wear. They have to be returned in darn near pristine shape or they pull more money. Much like not getting your security deposit back from an apartment. The other BIG issue with leases is what type of car you buy. Folks who leased a 1987 Buick GNX turbo probably got a killer deal. The buyout would have been based on a pretty standard depreciation, but the GNX held its value almost 100%. Conversely, leasing a used Cavalier is probably going to bite you in the butt. The car will be worth much less than the buyout most likely.