Learn Portuguese (Portugal): Ela quer visitar Lisboa.

When you have two verbs together to express wanting to do something, only the first one is conjugated. Quer is changed to match ela (she wants), and the second verb stays in its infinitive or dictionary form (visitar). This structure is just like English: 'she wants' + 'to visit'.

Why does the verb querer become quer? Shouldn't it end in an 'e'?

Querer is an irregular verb. While regular verbs ending in -er usually take an -e for the he/she/it form (like come for 'she eats'), querer drops that ending. So, it becomes quer instead of 'quere'.

Where is the Portuguese word for 'to' between the two verbs?

It is built right into the second verb! Visitar is the infinitive form, which means it already translates to 'to visit'. You never add a separate word for 'to' between quer and visitar.

Should there be the word a (the) before Lisboa?

No. In Portuguese, most cities and towns do not use a definite article (the words for 'the', like o or a). You just use the city name directly, so it is simply visitar Lisboa.