Learn Turkish: Şimdi öğrenmek çok kolay.

This is because of vowel harmony. The verb root is öğren- (learn). Since its last vowel is e, which is a front vowel, it takes the front vowel suffix -mek instead of the back vowel suffix -mak.

The English translation says "Learning", but doesn't öğrenmek mean "to learn"?

It means both! The -mak / -mek suffix creates a verbal noun, which turns an action into a thing. It translates to either the English infinitive ("to learn") or the "-ing" form ("learning"). Because it acts as a noun, it can easily be the subject of the sentence, as it is here.

Where is the word for "is" in çok kolay (very easy)?

In simple Turkish sentences that describe what something is or how it is, the "to be" verb ("is", "am", "are") is often completely invisible. Just putting the adjective çok kolay directly after the subject is all you need to say "is very easy".

Why does şimdi (now) come at the very beginning of the sentence?

In Turkish, words that tell us when something happens (like şimdi) usually go at the beginning of the sentence. Putting it first sets the time context right away for the rest of the statement.