Getting to Ukraine
The cheapest way to fly into Ukraine is through the Kyiv Boryspil International Airport. The main international hubs for these flights are Budapest, Frankfurt, Milan, Munich, Prague, London, Rome, Vienna and Warsaw with several flights a day of Austrian AUA, CSA Czech Airlines, LOT, Lufthansa, Alitalia, Air France, British Airways, KLM and MALEV - Hungarian Airlines; also Ukraine International, which code-shares on these routes with the respective carriers, and another Ukrainian carrier, AeroSvit. Special offers on flights come and go, depending on the whim of the carrier. Recently the low-cost airline Wizzair started operations within Ukraine and will start one international route from Kyiv to London Luton airport in December 2008. The only other low cost carrier serving Ukraine is AirBaltic, with flights routing through either Riga, Latvia, or Vilnius, Lithuania. AeroSvit could also be considered a somewhat low-cost carrier.
There are several airlines which offer direct flights to cities like Dnipropetrovsk (Lufthansa), Donetsk (Lufthansa, Austrian), Odessa (MALEV, LOT, Austrian, CSA Czech Airlines), Kharkiv and Lviv (LOT, Austrian Airlines), but they are more expensive.
To fly inside Ukraine, the most common airline is Ukraine International Airlines. It is the unofficial national airline, and its routes cover all of Ukraine's major destinations. Planes used are newer Boeing 737 aircraft. Aerosvit also recently introduced flights within the country from its hub in Kyiv, mainly flying newer Boeing 737 and 767 aircraft.
One can enter Ukraine by train from any land-bordering neighbor. When coming from Western Europe there will be a wait at the border while the train's bogies are changed in order to adapt to a different rail gauge. It's generally quicker and cheaper to buy a ticket to the border and then change trains, rather than wait getting through train. Generally, in Ukraine railway travel is much cheaper than flying, and is comparable (but probably cheaper) to bus or car travel. It will take at most a whole day to ride across the country, so unless you are in hurry take a train. It's good practice to take long-distance trains, which are much more comfortable. Avoid cheap third-class travel if you're cautious of local experiences.
The nearest significant town on the Polish side is Przemysl, and it's straightford to find by following route # 4 (which passes through Przemysl), also known as the E40 in European terms.
When you arrive, the road is fairly narrow (no motorway/autobahn this) with a queue of trucks and vans parked to the right of the road; a hard-core parking area with cafe/bar to the left. Don't stop behind the goods vehicles, slip up the side of them and then feed into the customs area when the guy flags you forward (for courteous Europeans, you're not jumping the queue - commercial traffic goes through a different process).
If you're in an EU registered car then make for the EU-passports, passport control section. Thence to Ukrainian passport control and then Ukrainian customs and then you're through. It used to be a nightmare, with apocalyptic tales of 5-6+ hours at the border (and as of July 2007, this is still a possibility), but the Ukrainians have made great advances in efficiency and it takes about an hour to make the crossing (September 2005 - still true in Feb 2006). Don't expect the border police to treat you in a friendly or even respectful manner, in fact, expect anything ranging from neutral to extremely obnoxious behavior.
Once through, just follow the main road towards Lviv on the E40 - this is the route right across Ukraine to Kyiv (and thence on to the East). Stick to this - the main towns on the way are Lviv, Rivne, Zhytomyr.
Watch out about 15-20 km inside Ukraine, I think the village is called Mostiska, as they have gone crazy about traffic calming measures here (speed bumps or sleeping policemen). They're like icebergs across the road, and very badly marked. And there are about four or five sets of them through the village. Other than that, take care on the road, which although the main East/West highway, and the main road route into the EU, still remains in a miserable condition (surface-wise). And you'll soon realise why Ukraine has such poor statistics in relation to driver and pedestrian fatalities and injuries. Drive defensively is the optimum advice re the roads, other road users and the walking, riding public.
There are inexpensive direct bus services to Lviv and Ivano-Frankivsk from Poland. They usually offer a budget level of comfort and cost about 90 to 100 hyrvnia (20 US$)
There are some ferries from Istanbul, Georgia, Varna (Bulgaria) to Odessa or to Crimea.