If one wants to daven Netz (at sunrise) how long of a period does one have to have caught this time? Is it only a few seconds, or longer?
The actual length of Netz is a little more than 2 minutes.
The MB in Biur Halacha 58:1 sv Kemo indicates that the time is at the beginning of Netz. (He also discusses the shita of the Rema who says Netz is about an hour, which he finds hard to explain based on facts. The Gr”a says it’s typo)
The Ish Matzliach in the middle of an extremely long Teshuva, (in the linked page, start at the bold words and go as long as you can) brings this time down, with all the different opinions if the time to start is at the beginning, in middle, or end of the Netz.
Practically speaking the Pnenei Halacha says the custom is to try to catch the beginning of Netz but not to be too overly concerned since there are plenty of opinions that give more time.