Well, it depends on what you mean. I assume you are from USA.
Obviously, you need to take a flight which is the least expensive way to get from US to Poland. There are many world airlines you can take; but the most popular is LOT the Polish airline. It doesn't mean the most popular is best though -- it depends on how picky you are :). In my opinion Lot is fine just to travel safely (they have new or newer planes), but if you need more comfort I suggest bigger airlines like Sas, British Airlines, or Lufthansa because these offer more for the same price. For example, what I don't like about Lot's aircraft is the fact that their planes have one big screen at the end of each corridor so if there's someone tall sitting in front of you, you usually don't get to see the screen and cannot watch a movie or something. But the food is good and stewardesses are nice too :). As far as I know, Lot doesn't offer free alcoholic drinks any more :(.
There are two major airports in Poland; the first and the biggest one is in Warsaw (Okecie), the other one is in Krakow (Balice). The Warsaw airport meets European standards as far as service standards are concerned. On the other hand, the Krakow airport is too small and it takes too much time to stay in lines (in my opinion). But they both are safe provided you don't "talk to strangers".
When you are at one of these airports you need to make sure to keep your luggage with you. I recommend not to trust guys whom you don't know and who seem to be too friendly; while most of the times they are totally harmless, some of them may not get you the best deal possible (especially taxi drivers or all kinds of "ushers"). As a result, I suggest you to actually KNOW where you're going to stay the first night when you get to Poland as it may be quite stressing and confusing for you to try to find an inexpensive and good place to stay on your own (assuming you don't speak Polish of course.
Even though it's generally safe to take a taxi, I suggest that you call your hotel so that one of their stuff picks you up from the airport. Tips are not obligatory in Poland; however, nobody will feel offended if you offer a tip :). Just do not take out in public a wallet full of money; it's always better not to stand out.
These are my two cents; I'll try to write more soon. Any other safety tips are welcome.