The Hans Wehr dictionary is a must have for people learning Arabic, but it is not organized in the same way an English dictionary is which can be confusing at first glance. For that reason I was months into learning Arabic before I bothered to figure out how to look up words. I don't recommend that. It's important to be able to look up words for yourself without having to ask the teacher and depend on their definition which (in my case) wasn't always correct.
In the Hans Wehr you can't go to the letter أ (alif) and find an alphabetical list of all the words that start with أ (alif). The dictionary is divided up into 3 letter verb roots, so if you go to the أ (alif) section you will find all the roots that begin with أ (alif). If you want to look up a word that is not just 3 letters then you have to be able to extract what the 3 letter root is. For words that are only 3 letters like رفع (to raise) then it's simple, you just search for them as they are, but for words that are longer than just 3 letters you have to know how to find the root of the word. For example, if you want to look up the word إستعجب (to be astonished) then you would have to know that the root is عجب and start looking under ع ('ain). If you tried to look up the word under أ (alif) you wouldn't find it, even though it starts with an أ (alif). Looking at the word إستعجب you might wonder, "How do I know which letters make up the 3 letter root?". Well it isn't hard to do with a little practice. The word إستعجب is measure X (ten). You can tell because it starts with إست. All measure X verbs will start with إست. Therefore, you immediately know that the إست is not part of the root. You're left with عجب which is the root.
So, once you know the root of the word you are trying to look up you flip to that root and you'll notice that there will be a transliteration of the root, for عجب it says 'ajiba. After that is goes into giving definitions. It has a few definitions, the roman numeral II, a few more definitions, the roman numeral IV, more definitions, the roman numeral V, definitions, and then finally it says X = V. This may look confusing, but it isn't with a little explanation. The definitions immediately after the root are for measure I. If you see the verb written as عجب then those are the definitions you are looking for. In this case it has written (to wonder, to marvel, be astonished, be amazed) and then it says the words that are commonly used with this word, من and ل, meaning that you would say عجب من or عجب ل basically meaning "amazed at". The roman numeral II signifies that the next definitions refer to the measure II verbs. If you see the very with a shadda عجّب then these are the definitions you want. The shadda on the second letter in a 3 letter root means that the word is in the measure II form. Then you have measure IV which is اعجب. The ا (alif) in front of the root signifies measure IV. Then there is measure V which is تعجّب. There is a ت at the beginning and a shadda over the ج. Then at the very end it says X = V. This means that the measure 10 and measure 5 have the same definitions. So, to recap, to find إستعجب we would look up عجب and go to the X. We'd see X = V and then look at the definitions of measure 5 and we'd know what the word meant.
All of the verb definitions are written right after the root. If the word you're looking up is a noun then it will be after the verb definitions. Sometimes you will have a word that has no root. In this case it will be listed alphabetically and you can look them up just like you would a word in an English dictionary. This includes any cognates such as country names or any word from another language. There is more to the Hans Wehr than just what is written here, but knowing this much will enable you to look up words and not be totally lost with the Hans Wehr dictionary.