It depends on what the new stuff involves. If it's details on already-decided features, just tell them "well that's going to take some more hours than already estimated," and if it's for things that are out of scope (design is a common one), just say, "that'll be extra." Have a sense of the scope and don't be afraid to tell them that will cost more. You should be able to explain the scope as you understand it and why the request falls outside of it. If you treat the agreed-spec like a checklist, it makes it much easier to clarify the amount of work you'll be doing.
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It depends on what the new stuff involves. If it's details on already-decided features, just tell them "well that's going to take some more hours than already estimated," and if it's for things that are out of scope (design is a common one), just say, "that'll be extra." Have a sense of the scope and don't be afraid to tell them that will cost more. You should be able to explain the scope as you understand it and why the request falls outside of it. If you treat the agreed-spec like a checklist, it makes it much easier to clarify the amount of work you'll be doing.