Learn German: Ich arbeite viel, aber ich schlafe sehr gern. - I work a lot, but I like sleeping very much.

Viel means "a lot" or "much". It stands alone to describe how much you do an action (ich arbeite viel). Sehr means "very", and it is used to make another describing word stronger. Just like in English, you wouldn't say "I very work" — you use viel for the action, and sehr to boost a word like gern.

The translation says "I like sleeping". Where is the word for "like" in the German sentence?

When talking about activities, German doesn't usually use a verb for "like". Instead, you use the action verb (schlafe) plus the word gern (gladly). Ich schlafe gern literally translates to "I sleep gladly", which is the standard way to say "I like sleeping".

Could I say ich schlafe viel gern to mean I like sleeping a lot?

No, that sounds unnatural in German. To say you like doing something very much, you must use sehr gern. The word viel (a lot) cannot be combined with gern.

Does the word aber change the word order in the second half of the sentence?

No, aber (but) is a friendly connecting word that leaves the normal word order alone. It takes up "position zero" in the sentence, so the subject (ich) is position 1, and the verb (schlafe) stays correctly in position 2.