There are several types of recipes:

Shaped Recipes are recipes, where it matters, which item goes into which slot. For example, you can't just arrange 7 iron ingots in any order to create iron leggings. The shape matters, thus it is a shaped recipe.

Mirrored Recipes are shaped recipes. Only difference is that the recipe can be mirrored along the horizontal or vertical axes.

Shapeless Recipes are recipes, where only the items you put in the crafting grid matter, whereas the shape is of no importance. For example, blue and yellow dye create green dye. This recipe doesn't care about where you put which item.

There are several ways of removing recipes.

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recipes.remove(output, NBTMatch);

This will crafting table recipes for the given output.
If NBTMatch is true, it will only remove recipes that result in items with the same NTB-Data as provided

Output is an IIngredient.
NBTMatch is a boolean and optional (Will be the same as false if not specified).

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recipes.removeShaped(output, inputs);

This one is more strict on which recipes to remove and will only remove shaped recipes that craft output with input.

output is an IIngredient
inputs is an IIngredient[][] (e.g.[[iron,iron,iron],[iron,null,iron],[iron,null,iron]])

Furthermore, inputs is optional. If omitted, the function will do the same as recipe.remove, though it will only remove shaped Recipes.
inputs can contain wildcard characters: [[<*>,<*>,<*>],[<*>,<*>,<*>],[<*>,<*>,<*>]] would refer a recipe whose items, as long as each slot is filled, don't matter.

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recipes.removeShapeless(output, inputs, wildcard);

This one is more strict on which recipes to remove and will only remove shapeless recipes that craft output with input.
If wildcard is true, it will remove shapeless recipes that craft output with input and other, non-specified items (for example you could disable all shapeless recipe that contain, among others, Lapis as ingredient).

output is an IIngredient
inputs is an IIngredient[]
wildcard is a boolean and optional (Will be the same as false if not specified)

Furthermore, inputs is optional. If omitted, the function will do the same as recipe.remove, though it will only remove shapeless Recipes.

Removes all crafting recipes in the game.
A bit overkill, don't you think?

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recipes.removeAll();

As 1.12 introduces naming recipes, you can also remove recipes once you know their name. You can also use regex to remove multiple recipes at once. And no, if you don't know what regular expressions are, I won't explain it here!

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recipes.removeByRegex("name[1-9]");
recipes.removeByRecipeName("modid:recipename");

You can also remove all recipes that were added by the mod specified.
You need to provide the mod's modid as string.

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recipes.removeByMod("modularmachinery");

Removes all recipes that contain specified ingredient as input

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recipes.removeByInput(<minecraft:iron_ingot>);

On 1.12, each added recipe requires a UNIQUE identifier, because the forge dev team wanted it that way.
This means, all add functions now require an additional parameter name at the start (which cannot be omitted).
This means recipe.addShaped(output,input); now is recipe.addShaped(name,output,input);
All other functionality stay the same. Remember that name needs to be unique!
name is a string.

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//pre-1.12
recipes.addShaped(output,inputs,function,action);

//1.12
recipes.addShaped(name,output,inputs,function,action);

This creates a shaped recipe for output using inputs as Ingredients.
If a function is added as third parameter, you can also use a function to determinate the output.
If an action function is added as forth parameter, you can also determine, what will happen, if the item is crafted.

name is a string and needs to be unique but is also optional output is an IItemStack
inputs is an IIngredient[][] (see below)
function is a IRecipeFunction. Please refer to the respecting wiki entry for more information on functions.
action is a IRecipeAction. Please refer to the respecting wiki entry for more information on actions.

inputs is a 2 Dimensional IIngredient Array.
So the recipe for Iron Leggings would be written as [[iron,iron,iron],[iron,null,iron],[iron,null,iron]]
If that looks to confusing, try splitting the arrays up into one array per line

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val iron = <minecraft:iron_ingot>;
val leggings = <minecraft:iron_leggings>;

recipes.addShaped("CTLeggings", leggings,
 [[iron,iron,iron],
  [iron,null,iron],
  [iron,null,iron]]);

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//Normal pre 1.12 syntax
recipes.addShapedMirrored(output,inputs,function,action);

//Recommended 1.12 syntax
recipes.addShapedMirrored(name,output,inputs,function,action);

Same as addShaped, only that the recipe created this way is a mirrored recipe.

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//Normal pre 1.12 syntax
recipes.addShapeless(output,inputs,function,action)

//Recommended 1.12 syntax
recipes.addShapeless(name,output,inputs,function,action)

This creates a shapeless recipe for output using inputs as Ingredients.
If a function is added as third parameter, you can also use a function to determinate the output.
If an action function is added as forth parameter, you can also determine, what will happen, if the item is crafted.

name is a string and needs to be unique output is an IItemStack
inputs is an IIngredient[] (e.g. [minecraft:dye:1,minecraft:dye:2])
function is a IRecipeFunction. Please refer to the respecting wiki entry for more information on functions. This is optional.
action is a IRecipeAction. Please refer to the respecting wiki entry for more information on actions. This is optional.

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addHiddenShapeless(String name, IItemStack output, IIngredient[] ingredients, @Optional IRecipeFunction function, @Optional IRecipeAction action);
addHiddenShaped(String name, IItemStack output, IIngredient[][] ingredients, @Optional IRecipeFunction function, @Optional IRecipeAction action, @Optional boolean mirrored);

This creates a shapeless recipe for output using inputs as Ingredients that is named name.
If a function is added as third parameter, you can also use a function to determinate the output.
If an action function is added as forth parameter, you can also determine, what will happen, if the item is crafted.
For the shapeless variant you can also set if the recipe is mirrored, if omitted, it will not.

You can use this to get a List<ICraftingRecipe> that contains ALL registered crafting recipes.

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recipes.all;

You can use this to get a List<ICraftingRecipe> that contains ALL registered crafting recipes for the given IIngredient.

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//recipes.getRecipesFor(IIngredient ingredient);
recipes.getRecipesFor(<minecraft:iron_ingot>);

You can use this to replace all ingredients in a recipe with another one, for example all sticks with stones. It also accepts an optional third parameter that matches agains the recipe outputs. If the recipe

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//recipes.replaceAllOccurences(IIngredient toReplace, IIngredient replaceWith, @Optional IIngredient forOutput);

//replaces every stick with stone
recipes.replaceAllOccurences(<minecraft:stick>, <minecraft:stone>);

//Explicitly uses any output, replaces gold ingots with gold blocks
recipes.replaceAllOccurences(<ore:ingotGold>, <ore:blockGold>, <*>);


//Only replaces in recipes with a diamond_sword as output
recipes.replaceAllOccurences(<ore:gemDiamond>, <ore:blockDiamond>, <minecraft:diamond_sword>);


//conditions work as well -> replaces in recipes for any recipe output except tnt
recipes.replaceAllOccurences(<ore:gunpowder>, <minecraft:tnt>, <*>.only(function(item) {
    return !isNull(item) & !<minecraft:tnt>.matches(item);
}));

You can even craft from inside recipes! The function will return an IItemStack or null depending if a recipe is found or not.

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//recipes.craft(IItemStack[][]content);
recipes.craft([[<minecraft:iron_ingot>]]);