It depends on the size of the values in the column you are adding. As David suggests the most accurate way of knowing is to create an index in a dev or test environment and see what effect it has there.
You can estimate though. If the added column is 8 bytes long (a
datetime column for instance) and there are 100M rows, then you can expect it to add approximately 800,000,000 bytes to the index's leaf pages. If it is a variable width column then you need to estimate from likely data lengths, or if you can run a query against the production DB you can read it from real data using
SELECT SUM(DATALENGTH(ColumnBeingAddedToIndex)) FROM TheTable.
This only accounts for the extra data added to the leaf pages in the index, but it should be accurate enough as an estimate as that will be by far the largest factor. There will be a little extra space taken by non-leaf pages too.
Also the above does not take compression into account, if that is enabled for your index. Compressed data can be much more difficult to model, so in that case you are back to testing by creating the index on realistic data as the only really accurate way to go.
Without knowing your table/index definitions it is not possible to give a more precise answer.