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I really hate dealing into an opponents hand, getting "ronned", houjuu, or whatever other term is used to describe that awful feeling I get in my stomach when my computer game, which has great voice animation, screams RON at me when I discard that winning tile. Having some vanilla ice cream around with chocolate syrup helps a little but playing better defense would help more.
Now that I am finally somewhat into defensive play, here's what I do if I decide to fold my hand due to an opponents riichi.
First, I discard all the tiles in my hand that the riichi caller has already discarded since they can not be claimed due to furiten.
I also toss the tiles the other two opponents have discarded after the riichi was called because if theirs weren't claimed, chances are mine won't be either.
Next, I try to discard tiles that I feel are relatively safe (but not always) regarding the riichi caller . For instance, if he tossed a 5, I might think that he doesn't have the 34 or the 67 so I would gamble on discarding the 2 or the 8, providing, of course, that at least one of each of those were already in someones discard pool. (never toss a tile that's not out at all, I think.)
I would also discard tiles when three of them are already showing on the table, except if it's an exposed pung. It might get claimed for a kong and a win on the supplemental tile, and then I would need some more ice cream.
EDIT: Latter part of above statement is in error. An exposed pon can't be extended to a kan by discard. See below.
Lastly, I would break up any pungs in my hand. If the first tile makes it through, I have two more safe ones.

After that, if by some miracle the game has not ended yet, win or draw, I don't know what to do. Suggestions?

For me, this gets even more difficult if it's nearing the end of the hand and all the opponents are damaten just waiting to pounce on me if I make a mistake. Then, I really don't know what to do, except maybe, keep going for the win. Oh, all those calories!

Note: Over the last 500 games (5,530 hands), I'm running a 9.6% houjuu rate. Have never seen any statistics on this but you take a chance every time you riichi,.....and I like to riichi.

A method I always forget to use is something (I think) called kabe.

An example would be:

If you know the location of all of the or be they in your hand, or in people's ponds, or whatever, then there is no way someone could have a tile shape waiting on the or , thus the more you can see on the table, the safer it is, since it can only be used in a shampon or tanki wait. So if you can see 3 on the table, the final one in your hand is safe.

If you only see 2, he could have a tanki wait, but yours is the one tile that can make him win, so it's called a one-chance tile.

Don't forget that a lot of this is based on the riicher having a ryanman wait.
One of my favourite things to do is to set suji traps, for instance, riiching off a 4 of a suit, while I'm actually waiting for a 1 or a 7
Be very weary of throwing supposedly "safe" tiles that are close to the dora,

One last thing to keep in mind, if you are folding your hand, and are worried about the other players being damaten, don't forget that if you can discard the tile the person before you did, do so, it's 100% safe as everyone else is in temporary furiten.

I'm no expert on these sort of things, but I do like to think that my defense is very solid.

Those suji traps come from having things like 4 6 8, riichi with the 4 and wait for the 7, or riichi with the 8 and wait for the 5.

BTW: An exposed pon can't be extended to a kan by discard.

Eagle1902- Good points, I tend to forget about Kabe and that damaten hint sometimes. I won't anymore.

Referee- Correct. I guess I rushed into that one.
An exposed pon can't be extended to a kan by discard.
I think I knew that but it came out anyway. Always appreciate you spotting these things.
You can
(1) make a kong on an opponent's discard when you are holding a concealed pung of the same tile.
(2) add a self-drawn tile to your own previously melded pung to make it a kong.

That's correct. And of course:

3) on a self-drawn fourth copy of the tile you are already holding a concealed triplet.

Another way to think of it, you cannot claim two tiles for a kong. If you claimed for pon, the fourth one you have to draw yourself.