Learn Russian: Жаркий день, и вода холодная.

In Russian, adjectives must match the gender of the noun they describe. День (day) is masculine, so it takes a masculine adjective ending (-ий). Вода (water) is feminine, so it takes the feminine ending (-ая).

The standard masculine adjective ending is -ый. Why does жаркий end in -ий?

This is because of the 7-letter spelling rule. You can never write the letter ы after the letters г, к, х, ж, ч, ш, or щ. Instead, you must write и. Because the stem of this word ends in к, the ending becomes -ий instead of -ый.

Since день ends in a soft sign (-ь), how do I know it is masculine?

Nouns ending in a soft sign can be either masculine or feminine, and you usually just have to memorize which is which. День is a very common masculine noun. Seeing it paired with the masculine adjective жаркий here is actually a great way to remember its gender!

Where is the word for 'is' in the second half of the sentence?

Russian does not use a translation for the verb 'to be' (am, is, are) in the present tense. To say 'the water is cold,' you simply say 'water cold' (вода холодная).