Give X $ or % Off

If you want to give for example 10% off the total cart you would leave Conditions empty and only set Actions:

Actions
Apply	Percent of whole cart if you want to offer a percentage Fix Amount of whole cart if you want to discount a fix amount
Discount Amount	Enter a numeric value, e.g. 10

BOGO - Buy X get Y free (same SKU)

See Buy X Get Y Free Tutorial

Buy X, get Y free (different SKU)

For this rule you need to define more in detail which products need to be purchased (Conditions) and which ones will be for free (under Actions).
If you want to offer "Buy two shirts, get one hat for free", you would define either the shirts category or the SKUs in your condition rules, and the hat category or SKUs under Actions. Set the Discount amount to 100 for Percent of Product Price Discount.

Conditions	Actions
If total quantity is 2 for a subselection of items in cart matching ANY of these conditions: CATEGORY is ...	If ANY of these conditions are TRUE : SKU is one of ...

Buy X amount, get % off

Conditions	Actions
Buy two or more 2 items: If ALL of these conditions are TRUE : Total Items Quantity equals or greater than 2	Get 10% off: Apply Percent of Product Price Discount Discount Amount 10

Conditions

Actions

Buy two or more 2 items:

If ALL of these conditions are TRUE :
Total Items Quantity equals or greater than 2

Get 10% off:

Apply Percent of Product Price Discount
Discount Amount 10

Free Shipping

If you want to offer free shipping for the total order you need to enable the Free Shipping Method and leave the Actions set to

0 Discount Amount
Apply to Shipping Amount > Yes
Free Shipping > For Shipping with matching items

If you don't want to offer Free Shipping, just enter as the minimum order amount "999999999" (without the quotes).