To create a formula that will give you the 18-character Id of records

Option 1

Classic

1. Go to Setup | Customize | object name | click Fields

a. For Custom objects: Setup | Create | Objects | object name

2. In the related list "Custom Fields & Relationships" click New.
3. Click the Formula radio button.
4. Click the Text radio button for 'Formula Return Type.'
5. Input the following Formula into the Formula Editor:

CASESAFEID(Id)

6. Set Field Visibility, add, or remove from the page layout.
7. Click Save.

Lightning
 

1. Go to Setup | Object Manager | Object name | Fields & Relationships
2. Click New.
3. Click the Formula radio button and click Next.
4. Click the Text radio button for 'Formula Return Type.'
5. Input the following formula into the Formula Editor:

CASESAFEID(Id)

6. Set Field Visibility, add, or remove from the page layout.
7. Click Save.

Note: When dealing with record types only custom record types have Ids. Please review Set Record Type Preferences for more information.

Option 2

The other way is to use the following Javascript as a bookmarklet in your browser to manually convert IDs any time.

1. Create a new bookmark
2. Name it something memorable (like "Salesforce ID Converter")
3. Add the code below to the URL
4. Save the bookmark

 Note: This may not work in the Edge browser.

javascript:(function(){
var input=prompt('Enter 15-character ID');
var output;
	if(input.length == 15){
		var addon="";
		for(var block=0;block<3; block++)
		{
			var loop=0;
			for(var position=0;position<5;position++){
				var current=input.charAt(block*5+position);
				if(current>="A" && current<="Z")
					loop+=1<<position;
			}
			addon+="ABCDEFGHIJKLMNOPQRSTUVWXYZ012345".charAt(loop);
		}
		output=(input+addon);
	}
	else{
		alert("Error : "+input+" isn't 15 characters ("+input.length+")");
		return;
	}
prompt('18-character ID:',output);
})();

To use the converter:

1. Click the bookmark
2. Enter the 15-character ID and click "OK"
3. Copy out the resulting 18-character ID

How-to Video: How to Convert a 15-Character Id to an 18-Character Id