Ég set glerið varlega í kassann, svo það brotni ekki.

-ið is the definite article suffix for neuter singular nouns in Icelandic.

• gler = glass (an uncountable/material noun, neuter)
• glerið = the glass
  So the sentence is talking about a specific glass (or a specific amount of glass) already understood from context.

With í (and several other prepositions), Icelandic uses:

• Accusative for movement/direction into something
• Dative for location inside something

Here you are moving the glass into the box, so it’s í kassann (accusative).
If it were already sitting there (location), you’d use í kassanum (dative): in the box.

kassi (box) is a masculine noun. In the accusative singular definite, masculine nouns often end in -ann (or -inn, depending on the noun class).

• kassi = a box (nom.)
• kassann = the box (acc. definite)

set is the 1st person singular present tense form of setja (to put).

• ég set = I put / I am putting
  Icelandic present tense often covers both simple present and present continuous, depending on context.

It’s fairly flexible, but some placements sound more neutral than others. Common options:

• Ég set glerið varlega í kassann... (very natural)
• Ég set varlega glerið í kassann... (possible, slightly more “carefully” focused)
• Varlega set ég glerið í kassann... (more emphatic/stylistic)

Adverbs usually go near the verb or right after the object, but word order can shift with emphasis.

brotni is the present subjunctive of brotna (to break—intransitive, “break” as something breaks).
After svo (að) meaning so that / in order that, Icelandic commonly uses the subjunctive to express purpose/desired outcome:

• ...svo það brotni ekki = so that it won’t break / so it doesn’t break

In casual speech/writing, you may also see svo að explicitly: svo að það brotni ekki.

In subordinate clauses like svo það brotni ekki, it’s very common for ekki to come late, often after the verb.
This placement is normal and idiomatic:

• það brotni ekki = it not-break → it doesn’t break / won’t break

A rough guide (accent varies by speaker):

• Ég: sounds like yeh (with a light y sound at the start)
• glerið: roughly gleh-ri-th (final ð is like the th in this)
• kassann: roughly kah-san with a long-ish n sound at the end
• brotni: roughly brot-nih (the tn cluster is pronounced tightly; many speakers make it sound a bit like dn in flow)

If you want, I can give a more detailed IPA version too.