My Dad has a second home that I've made significant investments in by expanding/improving. The deed of the house is currently in a Real Estate Trust that he had the property under for a number of years before the improvements. We now would like to recognize my investment in the property by adding my name to the deed, title or both. Can you provide some guidance on what needs to take place?

Is he a trustee with a bank? Is it revocable or not? Is he elderly or ill?
Your best bet is to talk to the trust bank with him.
One easy way to recognize you is to simply change his will to reflect the work you did, keeping in mind no-inheritance tax limits and changes coming on same.
The trust can sell or gift you portions of the property, but you have to pay the usual revenue and other taxes due when a deed is changed, and gifting is taxed over 13K worth a year.