If you know some basic Hebrew (surely if you've taken Level 1 of our program), you know how to say he is walking - הוּא הוֹלֵך (hoo hoh-LEKH).
To say he is wandering, you'd use הוּא מִתְהַלֵּך (hoo meet-hah-LEKH). This is a reflexive התפעל (heet-pah-EL) usage of the root ה.ל.כ. In Modern Hebrew, the word is often used facetiously, as in הָעַכָּבִישׁ מִתְהַלֵּךְ לוֹ בַּחֶדֶר שֶׁלִּי (hah-ah-kah-VEESH meet-hah-LEKH lo bah-KHEH-dehr sheh-LEE) - The spider is wandering around my room!
This word comes straight from the Bible. It appears in God's commandment to Abraham, קוּם, הִתְהַלֵּך בָּאָרֶץ (koom, heet-hah-LEKH bah-AH-rets) - Get up, traverse the land!, further immortalized in the song below. (can't see the video?)
The word also appears in this week's Torah portion read by Jews around the world (see this link, verse 19).
שבת שלום וסוף שבוע נעים לכולם - Shabbat Shalom and a good weekend to all!