Learn Russian: Эти сапоги тёплые.

When saying 'This is a boot' or 'These are boots', you use the fixed word это (Это сапоги). But when you say 'these boots' as a combined phrase, the word for 'these' must match the noun in number. Since сапоги is plural, we use the plural form эти.

What is the singular form of сапоги and why does it end in -и here?

The singular is сапог (a boot). To make masculine words plural, you usually add -ы or -и. Because of the Russian spelling rule that says you can never write the letter ы after г, к, х, ж, ч, ш, or щ, we must add -и to get сапоги.

Why doesn't the adjective тёплые have the exact same ending as сапоги?

Adjectives and nouns have different sets of endings, even when they match in plural number. For most plural nouns, the ending is -и or -ы. For plural adjectives, the standard ending is -ые (or -ие). So, тёплые is the regular plural form of the adjective тёплый (warm).