Output Radio or Checkboxes with A+M Forms
I'm confused by what you mean by "output". Do you mean: how do you write custom HTML for checkboxes or radio buttons and have them submit to amforms?

If that's the case, you need to understand the name attribute always needs a fields[] array. StraightUpCraft has a great rundown of how all field types' name attributes should be formatted in order to submit to Craft, no matter if you're using amforms, Sprout, or whatever.

Radio Buttons

Radio buttons are a "single option field", meaning that when the form submits, only one value goes through. Your code should look like this (I stripped out some of the unnecessary markup):

&lt;label&gt;Choose an option
    &lt;input type="radio" name="fields[fieldHandle]" value="Option 1"&gt; Option 1
    &lt;input type="radio" name="fields[fieldHandle]" value="Option 2"&gt; Option 2
    &lt;input type="radio" name="fields[fieldHandle]" value="Option 3"&gt; Option 3
&lt;/label&gt;


Checkboxes

Checkboxes are "multi option fields", meaning that when the form submits, any number of values can go through, so you need to submit them a bit differently:

&lt;label&gt;Choose your class type
    &lt;input type="hidden" name="fields[fieldHandle]" value=""&gt;
    &lt;input type="checkbox" name="fields[fieldHandle][]" value="Option 1"&gt; Option 1
    &lt;input type="checkbox" name="fields[fieldHandle][]" value="Option 2"&gt; Option 2
    &lt;input type="checkbox" name="fields[fieldHandle][]" value="Option 3"&gt; Option 3
&lt;/label&gt;


Pay close attention to each input having an extra [] at the end and the hidden input that collects all their values into a final array.



One very important note

You absolutely need to make sure the values of each input you have in the HTML equal the values you created in the CMS when you created the field. This includes capitalization and spaces.  So if your checkbox field in the CMS, for example, had a handle of breakfast, and each option's Label/Value was set like 


French Toast | French Toast
Ham n' Eggs  | ham-n-eggs
Corn Flakes  | c0rnFlaaaake$$


then your input values need to match exactly:

&lt;label&gt;Breakfast Options:
    &lt;input type="hidden" name="fields[breakfast]" value=""&gt;
    &lt;input type="checkbox" name="fields[breakfast][]" value="French Toast"&gt; Option 1 (this text can be anything)
    &lt;input type="checkbox" name="fields[breakfast][]" value="ham-n-eggs"&gt; Option 2
    &lt;input type="checkbox" name="fields[breakfast][]" value="c0rnFlaaaake$$"&gt; Option 3
&lt;/label&gt;


Craft's expecting these to line up, and if they don't, then either these fields' values will be ignored on submit or, if the field is set to required in the CMS, you'll get a back-end validation error.