Latin had a manner of punctuation, though it wasn't used consistently.

One way of breaking up sentences through the use of postpositives. A postpositive is a conjunction that always is the second word of the sentence, signalling the previous sentence had ended. Words like tamen, autem, enim, quidem, ergo, vero, igitur.

In some inscriptions, Latin also uses dots to distinguish between words, rather than spaces. For instance, this bronze inscription of a speech by the emperor Claudius uses dots to separate words. The surviving portion of the lex de imperio Vespasiani uses the same convention.

There are also enclitics like -que - which means "and" - that get attached to the end of a word. The others are -ue, -ne, and -ce. The most famous use of an enclitic is probably the opening line of the Aeneid: Arma virumque cano." "I sing arms and the man." That -que is telling everyone that virum and cano are different words, though virumcano wouldn't make any sense in Latin anyway.

So while Latin didn't use spaces, it has a number of tools to clue readers in as to how a sentence is meant to be read.