Is it supposed to be hard to find an affordable used car?

try several reputable dealer ships....

If you have $4K, you have enough for a down payment at a reliable dealer. And when I say RELIABLE DEALER that's what I mean. Don't answer ads and don't look for cars being sold by private owners. You can't count on those being reliable cars. Go talk to a few dealerships. Apply at those who have the best customer ratings.  Do some homework first--find out what kind of car you're looking for, how much you will drive it, look up the reliablity of the vehicle and the cost to run it. Most dealerships have online search functions. You put in your information and they will come up with a list of cars you can probably afford. Give them $2K down--and finance the rest. If you can afford taxis every day, you can afford a modest payment on a car, and the maintenance and gas/oil you will need. 

And do your research! It pays off tremendously when you go car shopping. Don't be fooled by pretty, flashy cars--look for something that will be economical to use and keep. 

I have only bought 3 used cars in 58 years.  They are too expensive compared to new ones.

hard to find , no there easy , just getting a reliable one is hard .

You NEVER do websites.   Many people still are not into computers so many do it the old fashion way.  Either the car is out front lawn with a price tag and for sale sign on it or it is in the back garden.  They have not gotten around to that car yet.  That will be the cheaper one. Right now the chickens use it as a hen house. So you got some hay & dropping to clean out of it, but it runs & you always wanted a van, right?

 Or a rusty Toyota.  The rust cancer holes do not matter so long as the car runs well.  It pays to have friends who know of friends so a bunch of extra eyes out there looking for you... for possible car choices.  I know a few mechanics so, they are always running into cars...up for sale.  Or they know of another mechanic who knows.    People are not on line and because of that the prices are more reasonable.  If it is a high price it is because they will sell it "if they get that price"  Realistically, they know the car is not worth that, but people are hard up for money...and as we head toward the Xmas season, they are NEEDING THE CASH.  No one is buying, they got RENT &FOOD TO BUY. It is becoming a buyer's market.  The seller's HAVE TO SELL, the buyers don't have to buy...until it is a sweet deal.

Everyone would like to find a cheap but good car.  $4000 is a significant amount of money, so you should find a number of possible cars.  Best to spend less and save some for unexpected repairs.  

     I almost traded in my truck 4 years ago for $1000.  Deal fell through and I am still driving it.   Would you have bought it for $1000?  Looks like it went through a hail storm.  The tires have been replaced and the windshield too .  About $1000 dollars of repairs over 4 years.  Now the fuel pump has gone... Another $1000, but it should last for several more years.

     Some of the best cars I have bought were the absolute cheapest.

One was $50 and came with the back seat filled up to the windows with composting leaves.  Drove it for a year and sold it for 10 x's that amount.

       The very best deal could come from some aging relative that loves you and would never take advantage of you.

If you find a car you would like to have, make an offer, regardless of the asking price.

You get what you pay for.

$4K is a very small sum to buy a car with. Plus, if this is to be your first car, have you priced out the insurance that you WILL have to buy and pay for ? I'm betting not.

Take the bus, walk, ride a bicycle.

Its not a walk in the park with only $4k to spend. But avoiding dealers is a good start. You might want to get your license before you buy a car. Another poster said go to "reputable dealerships".

There ARE NO REPUTABLE DEALERS than sell $4000 cars.  smh

For only $4K, you will naturally need to spend a LOT of time looking before you find a car in reasonably good shape. It's not impossible but, yes, it's hard. Since you know so little about cars, it's entirely possibly you won't recognize a good car if you see it. Nor will you recognize a terrible car when you see it. You need the help of someone who has experience and knows what they are doing, as well as a mechanic who can inspect any car you think you might want to purchase.