Learn Dutch: Probeer het en loop verder. - Try it and walk further.

This sentence is giving commands, which uses the imperative mood. In Dutch, just like in English, you usually drop the subject pronoun for commands and simply start with the verb stem (probeer, loop).

The dictionary form of "to walk" is lopen. Why does it change to loop with a double 'o' here?

To make a command, you use the verb stem, which is the same as the ik (I) form. If you just remove the -en from lopen, you get lop. To keep the long "o" sound from lo-pen, Dutch spelling rules require us to double the vowel when it ends in a consonant. So, it becomes loop.

How do we get the command probeer from the full verb proberen?

It follows the exact same spelling rule as loop. When you drop the -en from proberen (to try) to find the stem, the long "e" sound needs to be preserved. So, the single 'e' becomes a double 'e', giving us the command form probeer.

Does verder literally mean "further" as in physical distance?

It can mean physical distance, but in this context, it usually means "continue" or "on". So loop verder means "walk on" or "continue walking". Adding verder after a verb is a very common way in Dutch to express that you keep doing a continuous action.