Athens airport is small affair compared with other European and American international airports- It was build right just before the 2004 Olympic Games, it has only one terminal, and it's very clean and functional.
Access to airport is easy via Metro and "Proastiakos" train from the center of Athens. You can use the same train lines to get to Athens from the airport or you can take a taxi. Taxis are parked in the lower level of the airport, in a "piatsa" (a taxi station). You have to wait in line and take the first taxi that pulls up. Keep in mind that all taxis in Greece are mid-sized cars and if you have too many pieces of luggage you might need to hire a second one, although most taxi drivers get very creative with the way they can stuff the suitcases in the trunk. Make sure the taxi driver starts the meter as soon as you start your trip, and be aware that there will be added several fees to the final fare (airport fee, excessive luggage fee, etc - all posted on a list that's displayed in front of the passenger seat.
If you have to drive and part at the airport, you will access it via the Athens "beltway" called Attiki Odos. It is a toll, multi-lane road (toll rates 2.80 Euro) that gets congested only during rush hour traffic, and it can take you to the airport in short amount of time.
Airline counters open about three hours before a flight and you have to watch the announcement boards to see which counter servers your flight. Certain airlines have automated check in machines where you can scan your ticket and pick your seat. You still have to wait in line to check in your luggage though.
You will find money exchange machines in the lobby, and luggage carts are lined in in automatic dispensers outside the airport (one euro).
There is small museum upstairs, and to your right as you enter through the main departures gate. It exhibits artifacts unearthed during the airport construction. They range in age from 3000 BCE to Byzantine years. This is probably the most quiet spot of the airport, and it's not unusual for passengers with long layovers to unroll their sleeping bags for a nap around the museum. It's not an official camping area, and it is probable that security might ask you to move on. Waiting areas have comfortable seating, even though some gates get really crowded, most chairs don't have arm rests, so it's possible to lay down if desperate.
Once you check in, there is small shopping area with several newsstands/cafés/restaurants right behind the ticket counter line, but there are more shops beyond passport control and entry into the transit/duty-free area. Just like in every other airport, there is a plethora of restaurants and places to have a coffee. Once you pass through security and head towards your gate, shopping is limited. Some gates have a kiosk with snacks and water (which you can take on your flight), and some have just venting machines with water and soda (need coins).
There are clean bathrooms everywhere, and the quieter and less busy ones are closer to the gates (even though they are smaller).
Internet access via wifi is spotty. There used to be free Internet everywhere, but now it's no longer the case and you have to sign up for the service if you don't have your own access through your telephone.
If you travel with a pet and you need an area for your pet to do it's "business", you will find some limited grassy patches right across from exit at the lower level. If you are in the Departure area, you will need to take the stairs to the lower level (the Arrivals area) and walk out across the two way street. See Athens airport on the map
Very rarely passengers would arrive at Athens via boat, but if you do, chances are that your boat will dock either at Piraeus, or Rafina, or Faliro (rarely).
From Rafina you would need to hire a taxi to take you into Athens. It's a half-hour drive but it can take double and triple that time if you encounter traffic.
From Pireas, you can catch the HSAP train at the Pireas station that connects with all the Metro lines, so you can easily reach the center of Athens. Depending on the location of your ferry, you might have to walk a long way to get to the station. The boats that connect with the Dodekanesse islands and Crete dock far away from the station, and you might want to take a five minute taxi ride instead of a twenty minute walk in the heat. Other boats dock much closer to the station so walking to it should not be an issue (see the to orient yourself).
If you arrive to Greece via ferry from Italy, your best bet would be to disembark in the town of Patra. From there you can take a bus to Athens. The ferry companies offer their own bus service and you can buy tickets at the ferry reception area during your trip. If you prefer the public bus lines, you would have to take a taxi from the port of Patra to the bus station and wait for the bus to depart. Piraeus port map
If you arrive to Athens by bus you will get off at the main station, most likely the one at Kiffisos (see it on the map). From there, the best way to get to your final destination without getting lost in the labyrinthine public bus schedule, is to hire a taxi. There is a long line of taxis waiting for passengers in the station. Wait in line and take the first taxi at that station (it's illegal to flag a taxi that's not in that line).
If you are leaving for a destination via bus from Athens, you will still use the same station, and the best way to get to it from your hotel is also via taxi. Once at the station, you need to find your bus line. It's a small station but if you have luggage it would be best for one person to wait at a spot with all the luggage while another walks around to find the bus. Allow some time before you bus departs because the buses leave on time and Athens traffic might prevent you from reaching the station in a timely manner.
The bus station itself is not built to cater to tourists. The intercity buses are the main mode of transportation of ordinary Greeks and you will actually get a taste of "real" Greece just by hanging out at the station. It's a safe place with ample police presence who would perform random ID checks (mostly looking for illegal immigrants) and very rarely luggage checks.
There are many kiosks that sell drinks and snacks all around the station, and a main ticket and eating building at the far end. The restrooms are located at the basement of that building, and are to be used only in dire emergency.
It is possible to buy tickets on the spot (at the ticket counter) but in July and August you should book your bus trip ahead of time because seats are sold out more often than not. Tickets are usually a bargain compared to other modes of transportation, so bus hopping around Greece could keep you under-budget.
You will have to check you luggage. Right next to the parked bus that you plan to travel with you will find a scale and someone who can weigh it, tag it, and put it in the bus stowaway area. Stay with your luggage at all times and note which side of the bus it has been put in so you can easily get it when you get off at your destination. You can take a small backpack in the bus cabin, but storage there is limited.
Be aware that most employees of the bus station won't be speaking much English (or any other language), and that's especially true for the bus drivers and the luggage handlers around you bus.
The main train station is much closer to the center of Athens than the bus station, and it's well connected with the Attiko Metro (the Athens subway), albeit you would have to walk across a very busy road to the metro station. There are plenty of taxis also waiting in line for arriving passengers. Always wait your turn and take the first taxi in line.
Trains in Greece are notoriously inefficient so not many tourists prefer to travel that way. To get to the Peloponnese from Athens you should use the Proastiakos train, although we'd recommend taking a bus to your final destination. For all other destinations, service is limited to and from Athens main station, so unless you travel to another major city like Thessaloníki, you'd be better off taking but bus as well. See the train station on the map