To save a few dollars when you travel around Ukraine you need to do your homework first. A few tips that can save you money is to use local transportation such as the bus or Metro. Taxi drivers can spot a tourist in a second and will charge as much as they think they can get. The locals always negotiate a rate before a ride. Since most people arrive at KBP we will tell about how to get to Kiev from there. You will be using the bus and the metro to get to Kiev, the bus from the airport is 25 grivna, to get local currency go to terminals A/B and they have a place to exchange a few dollars to grivna. The bus will go to the train station where you can take the metro for 2 grivna each way. The name of the train station is vokzal or vokzalna you should spend some time learning to read a little Russian.
The metro has signs in English so as long as you know where you are going there should be no problem, there is a map on our Kiev page to help. I use my map on my iphone to find where I need to go. If your phone is unlocked you can buy a local sim card and data for your phone, I use MTC for local sim. The cost is relatively cheap in Ukraine compared to most places. Most places who rent out apartments will offer to have a taxi meet you for around 35 dollars and if you have a lot of baggage you might consider it. Most rental company's who cater to tourists offer Wi Fi and renovated apartments with hot water on demand (check our links page).