Here are two copies one from the other forum which is very straightforward. The second one copied from this forum a while ago is more detailed but only shows directions to Condado. Hope they're of use.
Lynn
DIRECTIONS FROM ALICANTE AIRPORT TO CONDADO
Head on A7 to Murcia then after Murcia this becomes A7 to Almeria and Grenada.
Turn off at Junction 627B - Mazarron RM2.
Turn off the RM2 at Jnc 4 - Mazarron RM23.
Condado is Jnc 7 on RM23.
DIRECTIONS FROM CONDADO TO ALICANTE AIRPORT
From Condado the simplest and fastest route is; Out from Condado, turn north on RM 23 towards Alhama de Murcia. After 4 kilometers, turn north on RM2 towards Alhame de Murcia. After another 4 kilomters turn right towards Murcia on A7/E-15. Just stay on this road for about 95 km and there is a sign for the airport. It is appr. 3 kilometers from the motorway to the airport.
This is the other one we copied, it goes into more detail, but this is only from the Alicante airport.
Turn right out of the car hire car park, at the junction (which won’t be far away) turn immediate left, this will put you on the correct road no slip roads to deal with, follow the signs for Granada/Almeria/Vera AP7/E15 you will probably not even notice you have joined the A7.
The road will signposted A7 Murcia/Almeria/Granada (if in doubt just follow signs for Almeria/Vera as they are way past where you need to be).
Continue to Murcia City approx 40mins
Stay on the motorway and as you come to Murcia City continue to follow the signs for Almeria/Granada, there will also be a yellow sign in Arabic with a picture of a ship on it, for the port, shortly after this the A7 veers right at this point. It will look like you’re coming off the road, but it is still signed A7 Alhama de Murcia/Almeria/Vera
Continue on the motorway heading for Alhama de Murcia/Almeria.
As you near Alhama de Murcia look for Junction 627 (approx 20 mins away from Murcia city)
Get into the Right lane for both the 627A/B. (The first turn off (627A) is for Alhama de Murcia).
Take the 627B exit which is immediately after 627A (it is a sharp right hand bend) – signed ‘Beaches de Mazarron’, ‘Mazarron’ & Cartegena’.
At Junction 627B you merge with the RM2.
Take the second exit which is junction 4 (it goes from Junction 1 straight to Junction 4 – missing out 2&3) for Mazarron and the road is the RM23 for Mazarron & Puerto de Mazarron
CDA will be signposted 3 miles along this carriageway, it has its own junction off the carriage way at the signpost CDA which takes you over the flyover and into the resort entrance. You will see on your left as you drive up the RM23 a long line of palm trees, these line the road that approaches the main entrance.
As you drive up the road there will be a huge sculpture on the roundabout in front of you with the name of the resort on it.