〜でも details
even N; N or something — marks a noun as a surprising case, or names it loosely as a suggestion
これくらい、子供でも分かるよ。
kore kurai, kodomo demo wakaru yo.
Even a kid could work this much out. casual
お茶でも飲みませんか。
ocha demo nomimasen ka.
Would you like some tea or something? neutral
Examples
even N — names the least likely member of a set to say something about all of them
これくらい、子供でも分かるよ。
kore kurai, kodomo demo wakaru yo.
Even a kid could work this much out. casual
そんな展開は、専門家でも予測できなかった。
sonna tenkai wa, senmonka demo yosoku dekinakatta.
Not even the experts could have predicted it would go that way. neutral
初めての方でも安心してお使いいただけます。
hajimete no kata demo anshin shite o tsukai itadakemasu.
Even first-time users can use it with confidence. formal
N or something — names one thing as a sample so the invitation or suggestion does not sound like a demand
お茶でも飲みませんか。
ocha demo nomimasen ka.
Would you like some tea or something? neutral
暇なら映画でも見に行こうよ。
hima nara eiga demo mi ni ikou yo.
If you're free, let's go and see a film or something. casual
分からないことがあれば、先生にでも聞いてみたらどうですか。
wakaranai koto ga areba, sensei ni demo kiite mitara dou desu ka.
If there's anything you don't follow, why not ask a teacher or someone? neutral
Formation
{N}でもattaches to noun格助詞＋でも（先生にでも・明日からでも・友だちとでも）attaches to noun phrase (schematic)
Notes
飲もう proposes tea, and the でも is there only to keep the invitation
from landing as a demand.
Related patterns
Similar
も simply adds the noun to others already in play (子供も分かる, children understand as well); でも presents it as the unlikeliest member, so 子供でも分かる is a claim about how easy the thing is, not about who else understands.
だって does both of these jobs too (子供だって分かる) but belongs to spoken push-back and complaint; でも is register-neutral, which is why a notice writes 初めての方でも and never 初めての方だって.
Lookalikes
With nothing in front of it, でも opens a sentence and pushes back on the last one ("but"); welded onto a noun it is this focus particle — 子供でも分かる is "even a child understands", never "but a child understands".
読んでも is 読んで＋も, and that で is the て-form ending, not this でも — which is why this one takes a bare noun, stacks after a case particle (先生にでも) and opens invitations (お茶でも), none of which a ても clause can do; the concession itself does line up (子供でも分かる ≈ 子供が読んでも分かる).