I am currently sending emails in Marketing Cloud but I would like to be able to see all of the emails that I sent on the receiver's particular record in Salesforce. Is this possible? If so, how do I do this? Thanks!
This is a standard feature of the Marketing Cloud Connector. It is built by default to transmit the tracking information back to Salesforce. Here's what you need to do
In Marketing Cloud - Tracking information will be sent to Salesforce only if you're sending the emails to Salesforce Data Extensions and your subscriber key is the Salesforce Contact ID. If your data extension is saved outside the Salesforce Data Extensions folder it would not send the information back.
In Sales Cloud - On the contact object - Page Layout - Add the related list "Individual Email results" to the layout, you can customize what fields you'd like to see. Also go to Marketing Cloud tab and check the settings to ensure Tracking Detail - Individual Level Tracking is enabled otherwise you'll not see data in the related list.
P.S. - I've mentioned the process for Salesforce contacts, you can replicate the same for Leads or Accounts based on your requirements.