Jigsaw , get the correct blade for what you are cutting , scribe a good easy to see line ( sometimes helps having someone else keeping the dust away as you cut, so you can see the line easily ), after you mark the line check underneath that it's all clear of bearers etc ( don't want to run over a section where the wood is thicker than the blade can cut ) , If it's not a cordless jigsaw have a practise run to ensure the lead is long enough and wont get caught up on anything, Keep the jigsaw flat on the surface with good downward pressureand go slow

have a spare blade handy , umm just in case
When you have cut it out a rounding over bit in a router gives a nice finish