Knots
-Always moisten your knot with saliva before pulling it tight. If you do not, it will not tighten as well and you might actually damage the line when you are pulling it tight.
-Practice tying your knots at home so that you can tie them quickly when you need to. Sometimes an extra 30 seconds can be a lot during a hot bite when the fish are moving through, and you want to be able to tie fast and securely when in a hurry on a rocking boat.
-After you have practiced and become proficient at some good knots, try to stick to those. A decent knot tied well is better than a fantastic knot tied poorly.
-The thinner the line, the more wraps you should make. Thin line knots slip much more easily than thicker line knots.
-Pull the knot as tight as possible.
-If you are in doubt about the integrity of a knot, always retie. A weak knot will slip at the absolute worst time, ie when you have a monster fish hooked.
Monofilament/Fluorocarbon Line Knots
Line-to-Lure Knots
Palomar Knot - a good non-bulky knot. It is one of the easiest knots to tie and with a little practice can be tied quickly on a rocking boat without looking. It maintains a very high breaking strength. I tend to use it on anything between 6lb to 60lb test line. See here for how to tie it: http://www.netknots.com/html/palomar_knot.html
Rapala Loop Knot - This knot is not as strong as the Palomar, but it allows for more freedom of movement for the bait or lure, which is sometimes important when fish are finicky. See here for how to tie it: http://www.netknots.com/html/rapala_knot.html
Uni Knot - This is the knot I go to for everything above 40-60lb test line. It is very easy to tie and very strong. See how to tie it here: http://www.netknots.com/html/uni_knot.html. I do 4-6 wraps depening on how heavy the line is. With very heavy line it can be hard to get more than four wraps.
Large Leader Knot - I'm not sure what the name of this one is, but you can use it for very heavy leaders, 100lb+. https://www.youtube.com/watch?v=2yNwC2MGDkU
Trilene Knot - This is the knot I use for smaller diameter lines up to around 15lb test. It takes a little longer to tie and you need to make sure you make enough wraps or else it will fail. If tied correctly it is a good strong knot though. See how to tie it here: http://www.netknots.com/html/trilene_knot.html
I can't remember the last time I had to use a knot other than one of those five when tying monofilament line to a lure or hook. Flurorcarbon is a little stiffer than monofilament but you can still tie all these knots with it.
Line-to-Line Knots
Whenever I have to connect one segment of monofilament to a segment of fluorocarbon or other monofilament, I use a uni-to-uni knot. It is easy to tie and holds well.
This site explains how to tie it: http://www.netknots.com/html/double_uni_knot.html
Other Knots
Dropper Loop Knot - This is very useful when you are fishing on the bottom. See how to tie it here: http://www.netknots.com/html/dropper_loop.html
You can either put the hook on the loop and hang the weight off the bottom or do the reverse if you are fishing for something like halibut that sit right on the bottom.
Drop Shot Knot - This is a very specific knot used for drop shotting (usually for Largemouth Bass). I do not know any other knot to use for this technique. See how to tie it here: http://www.netknots.com/html/drop_shot_rig.html
Bimini Twist Knot - This is used for creating a double line connection. It is very popular with the pros especially in Florida but I find it cumbersome to tie and have not really felt the need. However, it is so widely used that I would be remiss if I didn't include it. See how to tie it here: http://www.netknots.com/html/bimini_twist.html
Braid to Monofilament/Fluorocarbon Knots
This is one of the trickiest connections to manage. Some people use the uni-to-uni knot for this because it is easy to tie (rule of thumb is to use twice as many wraps for the braid side as you do for the mono). This works ok but is not ideal in terms of strength. However, if your leader is much lighter test than your braided line it doesn't matter too much. For example, if you are using a 15lb leader with 50lb braid it doesn't matter if your knot breaks at 30lbs of pressure because your leader would have broken by then anyway and you would never be fishing with that much drag with a 15lb leader to begin with.
My favorite braid-to-leader knot is the FG knot. If you tie it right it is very strong, and it has a very small profile so it doesn't bang through the guides when cast which is a huge advantage. See a video on how to tie it simply here. I recommend getting a line tightener for this knot: https://www.youtube.com/watch?v=ZPTzkep9xlI&t=194s
Braided Line Knots
Here are some other resources for knots:
http://www.netknots.com/html/fishing_knots.html
This site has quite a few fishing knots as well as helpful guides on how to tie them. They even have an app you can download for your phone. They also have other types of knots you might need such as rope knots.
http://www.animatedknots.com/indexfishing.php
Another good resource with over 170 fishing knots.
http://mysterytacklebox.com/learn/ever-fishing-knot-you-need-to-know
Another good source for knots with step by step instructions and videos.
http://www.epicwilderness.com/infographic-fly-fishing-knots/
This site has some great fly-fishing knot resources.
Here is another site with good knot info: https://www.hmy.com/the-ultimate-guide-to-fishing-knots-hooks-bait-and-lures/