Switching to a monolingual dictionary is something that isn't easy. It requires a lot of work, time and effort. However, the outcome is worth it. You're able to learn words without using your native tongue at all, allowing your Japanese to build upon itself. Many say that it takes a high level of vocab and grammar to be able to make the plunge, but I don't believe this. What I've found is that the grammar is incredibly simple and straightforward. I believe that a student of any skill level can use a monolingual dictionary to success as long as they keep their mind open.
First of all, which dictionary to pick?
The best dictionaries you can get are all free, thankfully. They are 大辞林, 大辞泉, 三省堂 web dictionary, and Google image search.
Just off the bat, my favorite is the 大辞林(だいじりん). It has very clearly written definitions with plenty of very good example sentences. The definitions are also ordered by the most common, so the first definition will probably be the one you're looking for (as opposed to the 広辞苑(こうじえん), which uses weird words, is expensive, and orders them based on their historical use).
大辞泉(だいじせん) is also decent, but I find it sometimes a bit weird. This could also be a personal preference, both dictionaries were written by the same author. Consider a definition from both dictionaries on a word I looked up recently:
The main definition tells you the exact same thing in the exact same words (いたずら doing 男 to the 女性, don't ask me to translate), but the 大辞林 gives something extra. In this case, it tells you that this happens in trains, or in night-roads and that sort of thing. I actually find this to be very helpful.
Now when you see this definition and you don't know what 夜道 means and you look it up, you'll probably get something like this:
Which is fine, but wouldn't simple google image search be much clearer and give a stronger association to the word?
Now, let's look at a word with 三省堂(さんせいどう) web dictionary. I looked up the word 憎む and got this definition:
Generally, 三省堂 likes to give one word definitions and oversimplified explanations. If you look up one word, often you will find that the definition is a single synonym. When you look up that word, the definition is yet another synonym. Using a dictionary this way, you would eventually reach a "safe" word which you do know (or the same words over again in a circle, in which case you are no better off then when you started), and learn that all the words you looked up mean the same as your "safe word". But in reality, there are very few true synonyms. The whole point of a word is that it means something different.
However, 三省堂 is not without its uses. When you run into a definition that is an entire mess, looking up the word in 三省堂 can tell you which words are important to a definition.
What do I do with this thing?
Use it a lot. The biggest difference between a person who is good with a monolingual dictionary and somebody who is bad with a monolingual dictionary is the amount of time they have spent using one. The basic vocab tends to repeat, the grammar is simple, and recursive searching gets less necessary over time. Sometimes when I have a very difficult to understand definition that I has many unknowns I'll add sentences for a word in the definition I looked up while skipping the original word. When I come across that word again, I'll have one less word to look up.
I guess all I have to say about using one is, don't be afraid. Know that in time it will be easier. Know that what you don't understand today will be easy tomorrow. When I started out, I took hours to figure out a single word. Where I am now, I understand most definitions immediately. I can honestly say that it was worth it.
Now that you're good with it, stop using it?
One concept I don't think is ever talked about enough is outgrowing the dictionary. I think that after a certain stage, the learner needs to free themselves from the dictionary. You may think it's mad, but quite a few polyglots even learn a different language without using a dictionary at all. After a certain point, reading constantly will give you the meanings from context. I personally have been doing this with success.
"If you know 4 words out of 5, the meaning of the fifth word is generally provided by the context. So, when you get to this point, the trick is to read as much as you can for a while, as swiftly as you can, tolerating the ambiguity of not understanding everything, fighting the impulse to look up every single word that you do not know. If you just read, read, read like this for several hours a day, every day for a few weeks or months depending on the difficulty of the language, you will find that your vocabulary has snowballed and that you have learned many new words from context without ever needing to look them up." - Professor Alexander Arguelles, a Hyperpolyglot who has studied 58 different languages and is an exponent in Polyglottery.
Consider it this way, if you want be fluent, why would you look up words in a dictionary when native speakers don't, and you don't in your native language? In your own language, do you look up every single word you don't know? I know I don't. The meaning is either clear from context, or it doesn't inhibit my understanding.
*Keep it in the same dictionary. When you look up a word and have to to some recursive searching to understand the definition, don't use a different dictionary for the other words. I don't know why, but I've found that it's best to stick to one dictionary when recursive searching.
*Google image search nouns and verbs.
*Don't rely on synonyms. Learn how words are different from each other.
*Don't forget to read and watch anyway.