Open the Contact or Lead record and scroll to the Campaign History heading.

Click Add to Campaign. A new pop-up window opens.

Use the Search Within dropdown list and Search field to locate the desired campaign. Next, click the Campaign Name link to select it.

Review the Campaign Member Edit page, which displays the Campaign and Contact/Lead names. Click Save when ready. 

Salesforce will add the Contact/Lead to the campaign and create a corresponding Campaign Member record.