If you want to add YouTube Subscription Button to your WordPress site you can use the following reference from Developer's section on Google.
https://developers.google.com/youtube/subscribe/reference
It's a matter of copy/pasting an HTML snippet of code.
The only small detail that you need to pay attention to is these two attributes.
data-channel and data-channelid.
data-channel <= that's your channel attribute
data-channelid <= that's your channel ID
Get YouTube subscribe button with your channel username
If you have claimed a username for your channel you can use data-channel attribute.
<br/>
Subscribe to our YouTube channel
<script src="https://apis.google.com/js/platform.js"></script>
<div class="g-ytsubscribe" data-channel="YOUR_CHANNEL_USERNAME"></div>
Get YouTube subscribe button with your channel ID
If you don't have a username for your channel you can use data-channelid attribute.
Here you need to specify the channel ID.
<br/>
Subscribe to our YouTube channel
<script src="https://apis.google.com/js/platform.js"></script>
<div class="g-ytsubscribe" data-channelid="YOUR_CHANNEL_ID"></div>
Here is how to get your channel ID