Pasting Adsense Into Source Code/HTML in WP

https://codex.www.ads-software.com/Theme_Development
https://yoast.com/wordpress-theme-anatomy/

there are plenty of template files whare you could add the ad code.

for a more detailed suggestion, you need to define more clearly where you want to have your ads to show in your site.

where do you access source code/html?

Also, is it possible to paste the html code from adsense in a text-box widget? I can’t get that method to work.

I’m using the “twenty ten” theme

where do you access source code/html?

the source code is php with a html structure; how to edit it, see here:
https://codex.www.ads-software.com/Editing_Files

Also, is it possible to paste the html code from adsense in a text-box widget?

yes, not a problem.
you might need to un-tick ‘Automatically add paragraphs’

I’m using the “twenty ten” theme

twenty ten will be overwritten with the next upgrade of your wordpress version – consider https://codex.www.ads-software.com/Child_Themes

there are plenty areas in twenty ten where you can add ads into the source code; however, the first step has to come from you – you need to clarify where you want the ads to show.

and don’t forget to search for a suitable adsense plugin.

I’ve had luck just pasting adsense code into text widget boxes, is there a reason you would have to use the adsense plugins?

there is never a reason to use any plugin if you can do the task without.