Learn Finnish: Kesällä perheeni purjehtisi uudella jahdilla. - In the summer my family would sail on a new yacht.

The base verb is purjehtia (to sail). Its stem is purjehti-. When we add the conditional marker -isi-, the two i's merge, making purjehtisi-. Finally, the "he/she/it" verb ending usually doubles the last vowel, but the conditional -i is a special exception and never doubles, leaving us with exactly purjehtisi for the family.

Why does the word for "new" look like uudella instead of starting with uusi-?

The dictionary form is uusi (new). A common rule you learned earlier is that Finnish words ending in -si usually change that ending to -de- when adding case endings. So uusi turns into the stem uude-, and then we add the -lla ending to match the yacht.

Why do uudella jahdilla have the -lla ending here?

The -lla/-llä ending (the adessive case) is used for locations, but it also translates to "on" or "by means of" for vehicles and instruments. Because the family is sailing on a yacht, the noun jahti (yacht) takes the -lla ending. Adjectives must always match the case of their noun, so the adjective gets it too.

We translate kesällä as "in the summer", so why doesn't it use the "in" ending (-ssa)?