I would like to thank my parents for... I would also like to thank the Rev. Smith who performed the wedding ceremony.
My new wife has said how much your joining us on this day means to us, and I also would like to add my words of thanks to you all.
In the first, 'also' relates to the 'thanking'.
In the second, where it comes straight after "I", it means, 'I too as well as (somebody previously identified" - in this example, the bride, the new wife.
'too' would be the better word, rather than 'also' in the second sentence.