Learn Russian: Весной погода хорошая.

Весной means 'in spring'. While весна is the base word for the season, Russian changes the ending to -ой (using the Instrumental case) to talk about the time when something happens, instead of using a separate word for 'in'.

Why is the word 'is' missing from the Russian sentence?

In Russian, the present tense of the verb 'to be' (am, is, are) is normally left out completely. You just place the noun (погода) directly next to the adjective describing it (хорошая).

Why does the word for good end in -ая (хорошая)?

Adjectives change their endings to match the gender of the noun they describe. Because погода (weather) ends in -а, it is a feminine noun. The adjective must match this by taking the feminine ending -ая, becoming хорошая.