To use your Avios for a straight points plus taxes reward flight redemption, you need to check the Aer Lingus availability on Avios.com. That is the portal for the Aer Lingus AerClub accounts when it comes to redeeming points for frequent flyer seats. As mentioned, usually there'll only be economy class available, because EI don't release many business class seats. Like any other programme, only a certain number of seats are put into award flight availability, usually there are five on Aer Lingus flights I've noticed, in economy, but it does vary.

To use points as part payment for a standard cash ticket, you will just need to transfer the Avios to your account and then book via the Aer Lingus website. At the end of the booking process is the option to part pay with Avios and what is shown to you depends on your Avios account balance. This does not rely on frequent flyer reward seats to be available

As mentioned, the part payment uses more Avios per dollar than it would for a straight redemption, but it's like that on all the airlines using Avios.