It happens to many players: they get to the river with a moderately strong or strong hand, they'd like to get to the showdown, so they don't bet, being content with a check-check-showdown situation. It's a mistake more often than not. More precisely: it's always a mistake, when the opponent shows a weaker hand in the end that he might have called a bet with. In these situations, we could have earned more chips, substantially more, as the biggest pots are obviously on the river usually, so it's the street we can earn the most on. The amount we can get with a nice valuebet on the river, assuming an average tournament hand with bets on all streets, equals 4 to 5 successful blind steals. It's easier to just get all those chips with one decision, instead of risking it over multiple moves.
So the answer for the first question is that we should always bet in position if it's likely that we have the best hand. We don't need to be absolutely sure about it, if it's likely, it's going to be enough.
The second part of the question doesn't have a more complicated answer. If the opponent check-raises us, most of the time we should just fold. We don't really have to worry about our opponents bluffing us as bluff check-raises are very rarely. Never miss a river value bet just to get to a showdown! The correct betsizing depends on multiple factors (which we'll talk about in an upcoming article), but as a general rule of thumb you can rarely go wrong with betting between 30-50% of the pot.
It's easy to just ignore this mistake as most of the time we are happy with winning showdowns. We often don't even see how big of a mistake we made because we usually associate mistakes with lost hands and chips. This is incorrect thinking; winning the pot doesn't make your play the correct one - you can still make mistakes without being the loser. Losing chips and missing out on winnable ones has the same impact on your overall game.
Imagine two friends talking during a tournament break. One inquires about how his buddy is doing.
Answer A: "I'm doing pretty good, I have 55k. I could have 70k if I didn't lose against a flush with my pocket kings."
Answer B: "I'm doing pretty good, I have 55k. I could also have 70k if I bet the river with my 2 pair when my opponent had a weaker 2 pair."
You'll hear answer A way more often. On top of this, it's very likely that "friend B" will be sipping his café latte satisfied while "friend A" won't be too happy with his stack. What's funny about the situation is that lets assume friend A played his kings correctly; he really can chalk it up to a lack of luck being unable to avoid the outcome. Friend B can only blame himself for being 15k chips worse off than he should be.
Never check the river impulsively without thinking, always consider betting on the river for value. Correctly applied river value bets are extremely important, they are invaluable elements of a prepared player's arsenal. Use it consciously, and as often as possible!