Landing cards are no longer required for most (European?) nationalities, so getting through passport control is now somewhat quicker than it used to be. As others have said, avoid the mini-cab drivers and pay no more than 200 UAH for a cab to the city centre. If you pre-book, the price can be as low as 150 UAH.

When arriving, you are most probably be transferred to the terminal in a bus because not too much ramps are there. Passport control is always overcrowded, be sure to fill the declaration sheet properly, or you'll have to wait again. Luggage - sometimes you have to wait for it for long and sometimes the locks are broken, don't check-in important/expensive things, better carry them with yourself. Very limited information desks, sometimes you have to ask other passengers or or airport staff guy, but people are usually very nice, in comparison to SVO or any other MSK airport. You can take a cab to downtown for some 200 UAH (20 EUR), don't be surprised if the driver asks for 500, just tell him that you know the price. (September 2010).
When you leave, duty-free store is perfect in the meaning of the prices. There's no free internet and coffee is quite expensive in the terminal.

Because there are only 3 ramps, in most cases you will be driven all over the tarmac in an airport bus. Once out of the bus, run to customs in order not to queue up for 50 minutes. There is a bus to Kiev train station which costs 25 UAH, on the right side when you exit the main building. The ride can take from half an hour up to 3 hours, depending on traffic. If you decide to take a cab to downtown, pay no more than 200 UAH. This is a decent price (June 2009). Kiev airport has a total of 10 gates, 2 bars and 2 tax free shops. Not much to do if you arrive neatly on time for your flight and have to wait for an hour. Bring a book or something to entertain yourself.

Arrived at Borispol along with 200 other passengers. At time 2 passport control stations were open but was quickly expanded to 6 stations. Do have your declarations form filled correctly or you will do it over. You can try to walk through green line at customs but do not be surprised if you are sent through red line. Red line customs were friendly and efficient. Once leaving secure area, pray you have pickup service waiting for you and not have to rely on the gypsy cab drivers waiting. Both arrival and departure lounges, as well as restrooms are very clean. Immediately outside you will be met by wall of cigarette smoke as smoking inside the airport building is not permitted.

Be prepared for a long wait through passport check. Also, make sure that your customs forms are filled out correctly and completely. While I was there, I had not filled out one part properly and after standing in line for 30 minutes, I was sent to the back of the line to fill out the sheet again.

Once through the passport check; head for the "green" line for customs check. I walked right through and never even had my bags looked at. There was a very long line for the "red" line.