If you are writing this as an offer or invitation then you should use 'would'. If you are confirming that you will do something (in response to a question) then you can use 'will'. Also, I like 'your' learning process, it seems more personal than 'the'. You can also omit 'process' and just say 'your learning' - which is more general and therefore includes the process

I would write it like this: I *would be* happy to help you *with the* learning process. You can contact me by email. You could also say “I’m happy to help with the learning process...” but it’s not as natural in that context. That would work better if saying, “Yes, I’m happy to do that.” So remember: “I would be happy to [verb]” for conversations like your example.

I think it sounds more english to say " I would be happy ..."