There's not much to it, just tap the buttons that appear.
Sometimes there's even a choice.

It's simple, put together better words than your opponent.

Each round your opponent will place down a word.
You must place a better word, or lose health.
The battle will continue until you or your opponent run out of health.

Use abilities to improve your word building capability.
Embrace bonuses to improve your word scores.
Use the wordbank to get suggestions.

Each opponent you face has words they use and words they are weak to.
Attacking your opponent's weakness makes your word far more powerful.

These are based upon WordNet's hypernym/hyponym relations.
Examples follow for illuminative purposes.
Let us consider an opponent weak to food.
Hit that opponent with 'pasta' to deliver double damage!

The word database used for this game is WordNet®
Nouns, verbs, adjectives and adverbs are grouped into sets of cognitive synonyms (synsets), each expressing a distinct concept.
Synsets are interlinked by means of conceptual-semantic and lexical relations.

WordNet superficially resembles a thesaurus, in that it groups words together based on their meanings.
However, there are some important distinctions.
First, WordNet interlinks not just word forms—strings of letters—but specific senses of words.
As a result, words that are found in close proximity to one another in the network are semantically disambiguated.
Second, WordNet labels the semantic relations among words, whereas the groupings of words in a thesaurus does not follow any explicit pattern other than meaning similarity.

There are loads of words that WordNet just doesn't have.
You can generally rely it on to have nouns, verbs, adjectives.
Any other class of word, don't be surprised if WordNet does not have it
After all, how would those words be worked into a hypernym/hyponym relationship?