(removed for privacy reasons) Colorado USA
(Please try to always include the diacritics on Szárföld. With a plain 'a', the first part is the word "sh!t".)
The easiest way to get to the records is to use the Catalog: https://www.familysearch.org/search/catalog
There are two sets of records on FS covering Szárföld. The Roman Catholic registers for Veszkény include people from Szárföld; they go all the way back to 1691: https://www.familysearch.org/search/catalog/123581
FS also has images of Szárföld's independent RC registers from 1869 to 1895: https://www.familysearch.org/search/catalog/122083
Note that only the baptisms have been indexed; marriages and deaths have to be found by browsing through the images.
The FamilySearch Research Wiki has very helpful information on how to find Hungarian records. Although the civil registrations began October 1, 1895, there are church records available to view online before that date. I have included the link to the Gyor-Moson-Sopron County, Hungary Genealogy page. Scroll down and you will see the church records databases listed with links so you can easily access those pages. I also suggest you click on the blue button at the top entitled Hungary Online Genealogy Records. That will take you to another list that may have what you are looking for. Good luck in your research.
The FamilySearch Research Wiki for Hungary Church records might be of assistance to you. Click on the link below and it will take you there.
Thank you all for your prompt and helpful responses.