Implementing Oauth1.0 from Apex involves passing a few parameters in the required format. Apex does support making a Oauth1.0 HTTP callout. Below is a screenshot from Postman, notice that the authorization has a bunch of token's and secret's.  Some are optional and we will see below how to pass them through Apex.

Consumer Key - Required

Consumer Secret - Required

Access Token - Optional

Token Secret - Optional

Signature Method - Required, usually it is HMAC-SHA1

Please note that the Access token and the Token Secret are optional, if you do have a token secret then the consumer secret will have that appended with a '&' symbol. For example,

Access Token Required => Consumer-Sercret&Token-Secret

Access Token not required => Consumer-Secret

Note that, every time the endpoint changes (you add new parameter values) you would have to sign it explicitly by calling the signRequest method.