Armory requires a Bitcoin node to sync to, so make sure you have a Bitcoin Core node running on your machine first of all.
Then let us know whether you made a paper backup (this is the easiest to restore) or just a copy of the wallet file. There are different instructions for recovering each as mentioned in this post:
Ideally, you should have your Armory "Root Key" paper backup somewhere... this would allow you to easily restore your wallet in a new installation.
Theoretically you could simply copy the .wallet file over to the new install, but I wouldn't recommend it unless you have no other option for recovery.
To get Armory up and running on the new computer, you'll need to:
1. Download the latest version of Bitcoin Core:
https://bitcoincore.org/en/download/2. Install Bitcoin Core and get it fully synced (do NOT enable "prune" mode!)
3. Download the latest version of Armory:
https://btcarmory.com/releases/ (currently v0.96.5)
4. Install Armory and run it
Once you have Armory+Bitcoin Core running successfully, let us know what files you have available to continue with the recovery.
Also there is a tutorial for restoring a paper backup here:
https://www.bitcoinarmory.com/tutorials/armory-basics/restore-wallet/