I have often wondered if I should ever ward my jungle to prevent my buffs from being stolen or smite my wolves. Also when and how should I ward the enemy's jungle without being caught?
Yes you should ward your own jungle because you never know when someone is going to invade. As for smiting the wolf camp I woulnd't say it is something you should do early, but once the tier 1 turrets (especially in mid) and even more so tier 2 turrets (once again especially in mid) then it definitely gains some value.
Warding choke points and entrances/exits of the jungle is always advised. You can never predetermine where any action is gonna happen between lanes, so the extra vision will help against possible counter jungling and even advise allies of incoming ganks.
As for warding the enemy jungle, you could slowly and procedurally encroach your vision from the river using 
and the smote raptors. Of course, this works best when you have allies who ward as well. That's in my experience at least.
Warding your own jungle is always a good thing. (Buying 
is a good investment. Stealing the enemy blue buff can be risky, but rewarding. In your jungle ward the baron, dragon, and major intersections or river entrances. Ward enemy buffs when its safe. If the enemy jungler dies and you see that their buff is online, go for the steal!
I like to use a 
in the bush near my blue buff. It rarely gets cleared out unless the enemy jungler invades with raptor buff.
I would say it really depends on how the game goes. If your team is dominating all over the place and every lanes are pushed all the way in to the inhibitor turrets, warding in your own jungle is just a waste. But if your lanes are pushed it, chances are enemy would try to sneak in a buff steal or camp a bush to make a catch. In that case, it wouldn't be too bad to have wards around.
yes like the chorus, warding is important, and ward your jg.... ward a lot... 4 wards on map at a time pink +3 means between u as the jg and the support + the rest of the team (hopefully) there will be about 10 wards on a map at a time giving some sight (this really is such an arbitrary number im picking, lots of people dont ward)
for the 2nd part of your post about warding the enemy jg, a wonderful way to feel safe is knowing where the enemy is, look at the mini map a lot.... a lot.... if you see all lanes r full then you are only worried about the enemy jg, now i wont tell you to just know where the enemy jg might be through experience, thats not an easy skill to learn but if they just tried to gank bot and failed, they prob are not at their red atm.... if ur near top, throw out some wards.... what im saying is after actions which let you know with some certainty where the enemy is, you are relatively safe to go a bit deeper
you can also ward hop for safety... its just tossing out wards in front of you as move in deep into fog of war, empty out all 4 of the wards from stone and get out recall....
assuming you are playing good side...now for learning where to put them, there are a lot of maps where players have shown where are good places to ward.... instead of just copying and pasting though i want to say think of the game as a tower defense, the enemy is moving through on paths of least resistance... means if dragon was done recently, there is less reason to be near dragon for a bit, it will not be as active as other locations all other things being equal.... so that means a ward in dragon pit is probably going to be a lot less useful than a ward up top tri bush where the jg might try a gank when u are pushing top lane...
also, in general, ward the intersections, these give u sight of many different paths, if the enemy is using a sweeper, then dont ward in obvious locations, if the enemy has destroyed your pink, dont put another pink right in the same spot right away... they will prob check it again.....
people are creatures of habit, they will vry often place a ward right where they destroyed a ward.... if you have a sweeper u now know where to go.... counter warding baby
If you have poor vision control and behind then smiting wolves is a good option. If you have an enemy jungler that counterjungles a lot (Nunu, Vi, Lee Sin), then it is also advisable.
If you start blue side you can go krugs smite with leash, then red, then wolves with smite and back. Now you have your jungle item and the smitten wolves protect your blue buff from being stolen.
Even when not playing the jungle role you will find me often throwing down a into friendly jungle to help defend the buffs. It's easier to defend the ward, as it's closer to your base and of course, helps you find out where everyone is.
