First Join the facebook group ´Almerimar Airport Transfer´ to see if any lifts are offered.

Almeria 

Bus:

Take the 333 bus@ 10.30 am from the green bus shelter outside Mercadona for the bus station in Almeria arriving around 12:00. Outside the bus station find the bus stop. The number 30 bus at around 12.20 pm goes to the airport.

VHF Net:  (When Running)
Ask on the channel 67 VHF net (Weekdays at 10:00) There is usually someone going in that direction either by car, share fuel costs, or taxi and share the fare.

Taxi: 
Around 60 – 80 euros – click > taxi  for a list of companies below

Ask Around: 
There are a few people who act as a private taxi service in the marina for around 40 – 50 euros.

Parking:
Of course, if you have your own car you can park at the airport. If you-prebook parking can be relatively cheap and the car park is just a few hundred metres from the terminal. The site to look for is [Arena] prices without a  promotional code is around 60 euros a week. You book online and are given a number. Collect your ticket from the machine at the barrier At the end of your stay you show the ticket and your booking number to the cashier and you will be charged the discounted price

Malaga

Coach:
Get a coach from El Ejido bus station. Check this site for the times on this site >[Coach]. I have found this a slightly difficult site to navigate so more reliable is to go to the bus station and pre-book a few days before. When you arrive at Malaga bus station I recommend taking a taxi to the airport for around 10 euros – or bus but can be difficult to find and often chaotic.

VHF Net:
As above, ask on the channel 67 VHF net (Weekdays at 10:00) There is usually someone going in that direction either by car, share fuel costs, or taxi and share the fair.

Taxi:
As above. Expensive, between around 150 – 300 euros, click > taxi  for a list of companies below

Ask around:
As above there are a few people who act as a private taxi service in the marina for around 120 – 150 euros to and from Malaga.

Or take your own car to the airport.

I found a super parking place – click the link > Red Parking – friendly, secure undercover parking and transfer lifts to the airport – a few minutes away – and thus running every few minutes included. I paid, in August, €16.50 for three days. 
(If you do use them the return instructions to find the courtesy coach are a little ambiguous. I quote from their instructions:
“On his return call when you have the luggage is in place of pickup. Terminal 2 arrivals (arrivals old, inside the tunnel.) Cortessy bus.” If you understand?
Tis in fact simple – when you know  – so, give them a phone call when clear in arrivals then turn right after coming through the main doors onto the street and follow the pavement for about 100 metres. Turn right into an enclosed road. After 300 metres the courtesy coach stop is clearly marked.)

Alicante

A long way, 330 kilometres .. click here Almerimar-Alicante to see options.
The best way if you drive, and cheaper if there are a few of you, is to hire a car at Almeria airport and arrange to drop off at Alicante. 

Ask around for people who do private taxi runs. Expect to pay around €200/300.