If you travel economy and cover long distances, you will several airports in one day easily.
On the way from St. Petersburg, Russia we went to Vantaa, Helsinki then O' Hare in Chicago and finally DFW in Dallas.
St. Petersburg International Airport is Pulkovo II (LED) is very small. There were screens projecting a bigger future Pulkovo III. Its size however never bothered me - it is very easy to navigate.
It has a Duty Free shop for the last minute souvenirs, a couple of bars for nervous travelers and a few places to eat. On arrival you just follow the crowd to Passport Control (equivalent of US immigration). There are a couple lines for the citizens of Russia and Belarus and the lines for visitors. If you are visiting you probably already have you arrival/departure record filled out (equivalent of US I-94). Keep the part that was given back to you by immigration officer. You will need it when you leave. I used to get very nervous about this procedure. Due to my Soviet past, I learned to feel guilty before the government whether I had a reason or not. Once a long time ago, a very strict lieutenant on the border told me: " Citizen! Stop smiling, I am comparing your picture". Things changed. Russians are not he smiling kind, but there is no hostility and people are polite.
Next, immediately after the passport control is the luggage claim. The one. It makes things easier. Once you are done sumo wrestling with your suitcase you can proceed to customs. Most of the time an average traveler has nothing to declare. Then you proceed through Green Corridor. If you are arriving from a different continent, you place your bags in the X ray machine. By the way, a lot of border and customs officers are women of stunning beauty. Stop staring and pick up your luggage on the other side.
You exit into Arrivals hall, where you can be greeted by your party, call a cab, exchange money and buy a local SIM card.
On departure everything is pretty simple as well, unless you are there during summer and boarding a Finnair flight (too many people going to the lakes and the woods, and the cottages).
You go through metal detector and X-ray luggage,. People, who are seeing you off can come too. Then again the Green Corridor for customs, check in line and passport control. There is one more screening before you board the flight, but it is very efficient and generally very respectful and painless.