Replacing internal hard drive

May567 wrote:

I feel comfortable with the physical install but just wondered what I need to do after it's installed to get it working and get my data back on it?

I know I need to back up too beforehand, and I currently do this with an external hard drive and time machine, but is this good enough?

First order of business, make sure you have at least High Sierra on your MBAir; and preferably at least Catalina. This is so you have the necessary drivers for new SSDs and the ability to format the SSD as APFS. Also, be aware that if you do not already have macOS Monterey installed, and you want to upgrade to Monterey sometime, you must install Monterey on the original Apple SSD first - so, do it before replacing the SSD.

If it were me, I would put the new SSD in an external enclosure, format it as APFS and install macOS on it, then use Migration Assistant to transfer apps & users from the existing internal SSD (still in place). When done, try booting from the external SSD. If all works well, then simply swap the new SSD into your MBAir. If you don't want to transfer apps & users, then just install macOS by itself.

At a minimum, to avoid complications, I would create a bootable macOS installer on a flash drive for whatever version of macOS you intend to use. At least then, if you run into problems, you can install macOS directly instead of having to rely on Internet Recovery.

May567 wrote:

I'm looking to replace the internal hard drive in my macbook air (11 inch,early 2015, 4GB memory and currenly 128GB storage looking to roughly double this) as its on its last legs.

MacBook Airs don't have internal hard drives, or room for them. They have SSDs. Other World Computing sells aftermarket "circuit board stick" SSDs that are compatible with your 11-in Early 2015 MacBook Air. I did not see anything compatible with your Mac when using the system selector on the Crucial site.

I don't know if the SSDs in your Mac are "bog-standard" or if they are of an unusual or proprietary type that only OWC would be likely to carry. (The types of SSDs in Intel MBAs and MBPs sometimes varied from year to year.)

Other World Computing – OWC Solid State Drives For MacBook Air 11" & 13" (Mid 2013 - Mid 2017)

I feel comfortable with the physical install but just wondered what I need to do after it's installed to get it working and get my data back on it?

You should make at least one external backup of your system, and have at least one external startup drive on hand, before doing the upgrade. Carbon Copy Cloner and SuperDuper! can make bootable clone backups – but if you're using Time Machine, you'll need to boot the Mac from something other than the Time Machine backup. You could do a "clean install" of macOS onto another external drive.

How to download and install macOS - Apple Support

As MartinR says, if you think you may EVER want to use Monterey, you need to install Monterey before installing the third-party SSD. I'm not sure that the installation has to be ON the original Apple SSD, but the Apple SSD has to be the one inside the machine the first time you (successfully) install Monterey. Otherwise when Monterey notices that you have old firmware AND a non-Apple SSD, the firmware update will fail, and the Monterey installation will, too.

And FWIW, here is information from OWC about SSD replacements for MacBook Air 11" & 13" (Mid 2013 - Mid 2017) models.

While other Mac models are designed to be user-serviceable, MacBook Air models are not.

It certainly sounds like replacement is your best option. Otherwise:

Mac Repair & Service