Do NOT stick your exposed leads into ANYTHING! The risk of shorting out is high, and you do NOT want to short out a LiPo because that is potentially dangerous.
You will need to buy some connectors and solder them on to the exposed leads.
Since your battery is fitted with an XT60 connector, you will need to buy a matching XT60 connector (probably the male version, as the battery comes with the female version I guess). For the connection ESC <-> Motor, you'll need to get some (female) bullet connectors.
For all connectors, make sure you get the ones that match your wire's gauge, and be sure to add some shrink tube over ANY exposed metal when done soldering and connecting the cables, so the leads - should they touch each other - will never short out or cause damage otherwise because they are now properly isolated.
If you are unfamiliar with soldering, my advice is to look up some info on soldering thick gauge wires. Here's some inspiration:
My avatar is what I look like after a "landing"...