Essentially just follow signs to the following ignoring the last oen as each new oen appears:

Athens
Elefsina
Korinthos
Tripoli
Megalopolis
Kalamata
Kyparissia / Pyrgos

If you fancy a rest/drink/food on the way from Athens there is a perfectly nice pit stop immediately after you pass through the mountain tunnel. After turn offs to Nafplio but before Tripoli. About halfway.
More detail is shown below:

Leave Airport towards ATHENS and pass big IKEA on your right.
A Directions from ATHENS AIRPORT to Kalo Nero

(3.5hrs lovely route, and no major towns to pass through, not even Athens)

few minutes after IKEA the road you want peels off to the right.
The Road you are after goes to ELEFSINA and KORINTHOS (Its called the ATIKI ODOS Motorway.)
As soon as you see signs for Elefsina / Korinthos follow them.
About 1 hour to Korinthos Canal & Korinthos exit (keep going straight past and now follow signs to Tripoli)
At division of road Take Tripoli turn to left NOT Patras to right
About 1 more Hour to Tripoli exit
Keep straight and just after Tripoli exit the road will cease to be so good and start to climb mountain
Go up and over mountain, along plateau for 20 minutes and over and down to Megalopolis which will appear in the valley below
On the outskirst of Megalopolis is a vilarea with garages & pitstops - its called Makrysi.
A sign indicates you are leaving Makrysi and enetering Magalopolis (there is a pitsop on your right called Georges Place).
Take the turning left here signposted Kalamata 53km.
You go around the edge of Megalopolis and stright on towards Kalamta.
Watch dangerous junction about a mile round where other Megalopolis road joins - priority not clear.
Follow road along and eventually up and down a mountain and through a place called Paradisia.
After you pass through a couple of places you come down the mountain, when you hit the flat you want the turning to KYPARISSIA and PYRGOS at the cross roads.
30 minutes down this road you will come to a T junction at Kalo Nero

PATRAS port after KALO NERO road crossing
DURATION: scarcely 2h

DITANCE: Patras, Pyrgos, Zacharo, Kalo Nero

If you left the port, bend RIGHT and follow a describing direction Pyrgos and drive always a describing afterwards. If you reached Pyrgos, drive please to Pyrgos in and follow then a describing direction Zaharo/Kiparissia/Kalamata. Please you call me with their departure of Patras and announce you please again if them through Pyrgos drove themselves.

ARAXOS airport after KALO-NERO road crossing
DURATION: scarcely 1,5h approx. 120km

DISTANCE: Araxos, Pyrgos, Zaharo, Kalo-Nero

They leave the airport area and drive straightforward. At the 1st you hold and follow yourselves road crossing RIGHT the road process. At the next road crossing you drive again RIGHT and are then on the main street after Pyrgos direction Zaharo/Kiparissia/Kalamata and follow this. If you reached Pyrgos, drive please to Pyrgos in and follow then a describing direction Kalamata.

Please you call me with their departure of Araxos and announce you please again if them through Pyrgos drove themselves

KALAMATA airport after KALO-NERO road crossing
DURATION: 45min

DISTANCE: Kalamata, Kalo-Nero

Please you drive some kilometers to you to the road process from the airport left and follow to a large crossing with traffic light device come and hold them there please further left and drive yourselves direction Tripoli, Athens, Kiparissia. They drive out now far only straight one and remain on this road approx. 28-30 km long to you to a sign coming, where it goes left to Pyrgos. There you turn accordingly. They drive on this road approx. 30 km to you at the crossing Kalo Nero are where it again left to Kiparissia go and right to Pyrgos. Drive they now please right raus. After a few meters is a baker's shop on the left roadside. Please they wait there. I am alike with them.

Please you call me with their departure of Kalamata.