initial steps:
1. go to
https://electrum.org/#download but verify that this is the real website and not a fake one!
2. download the appropriate version based on your OS
3. get the developer's PGP public key (learn how to verify PGP keys if needed) and get the respective signature of the file you downloaded
4. verify the signature using these 3: wallet file (.exe or .tar.gz or .dmg....) signature file (.asc) PGP public key.
recommended steps:
5. create a new Electrum wallet by selecting type of wallet you want (standard, multi sig or 2FA) which is one of the first 3 options
6. create a seed, back it up (on paper)
7. get an address from this new wallet and send your coins from your bitcoin core wallet to this address.
8. [optional] in case your bitcoin core doesn't work for any reason and you want to do step 7, after creating your wallet (step 6) from your menu select Wallet > Private keys > Sweep. then in the new window enter your private key(s) and after double checking everything click "seep" button at the bottom right corner.
alternative way (not recommended)
5. create a new Electrum wallet but instead of the first 3 options mentioned in previous step 5, you choose the last or 4th option called "Import bitcoin address or private keys" click next
6. enter your private key here (click the info button on top of this window for more information on how you should enter your key)
7. you have access to your funds and you can spend from the imported keys.