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When the Children of Israel constructed the Tabernacle, some of the tasks required doing very fine, delicate work – which seems to be beyond the technology that existed in those days. How for example were they able to carve out the names of the Twelve Tribes precisely into the stones of the High Priest’s breastplate (Exodus 28:21) or make golden strings (28:6,15)?
It’s a good issue. Although it’s possible the Israelites were more advanced than we think, the main answer to your question is that it was due to the existence of a special creature – a worm called the shamir. It produced an extremely corrosive substance which could burn through anything. It was held against the stones of the breastplate (as well as the stones of the apron (ephod) Aaron was to wear – see 28:9-11), and used to carve out the names of the tribes in the stone. As the Talmud (Sotah 48b) describes it, the artisan would write out the names in ink and then “show the shamir to them” (along the path of the letters) and the stones would immediately split apart. (Some suggest that “showing” the shamir to the stones implies that its stare is what split materials – implying it emitted radioactive or laser beams or some such.)
According to another opinion in the Talmud, the shamir was used in the Temple’s construction to cut and shape the stones used for the building. (See Exodus 20:21 about not using a sword (a metallic cutting instrument) on the stones of the altar. See also Talmud Gittin 68a.)
The Sages describe the shamir as an entirely miraculous creature. The Mishna (Pirkei Avot 5:6) states that it was one of the items God created on the Six Days of Creation immediately prior to Shabbat. (My teacher R. Yochanan Zweig explained that such items are really supernatural items, not belonging in the physical world, and so which theoretically should have been created on Shabbat. But since God refrained from creating on Shabbat, He created them the moment before Shabbat began.)
The Talmud describes the shamir further. It was only the size of a barleycorn, yet no material could stand before it. Even so, they were miraculously able to store it by wrapping it in tufts of wool inside a lead tube full of barley bran (Sotah 48b). The Mishna also states that as many other supernatural items, it disappeared with the destruction of the First Temple (Sotah 9:12).
See also here for an interesting article which considers if a recently discovered burrowing worm, native to the Philippines, could be the shamir.
In terms of your second question about the golden string, the Torah (Exodus 39:3) describes explicitly how the artisans manufactured it – by beating down plates of gold down until they were very flat, and then cutting them into strings.