Possibly the most important part of understanding Vedana, is that this is our initial reaction before we react verbally or physically. With the word "reaction", we are using it two different ways. Vedana is an automatic feeling which is actually a reaction to an experience. It's automatic, it comes due to past conditioning. Most Vedana is not really something that we're going to worry about changing, it just comes due to eye and form and eye-contact, for example. We see a tree, if we like the forest we have pleasant Vedana. If we like the city then we don't have pleasant Vedana when we see trees, we'd rather see buildings. There are people like that. With Vedana, it's automatic. To know Vedana comes right before our reactions of liking, disliking or neutrality, that's probably the most important part about working with Vedana.
When walking into the meditation hall, some people come in and see that they've lost their favorite sitting spot, it's eye and eye-contact with a sight. OK, that's what's happening, you walk into the hall, your eye sees a sight, you have eye-contact, consciousness understands that it's seeing something and you have a Vedana arise. For some people it's unpleasant, they have lost "their" spot. That can come, that's not really a big problem in the moment if we don't react. If we see unpleasant Vedana and we recognize "Unpleasant Vedana, unpleasant Vedana", any mental notes you want, and then we just go about looking for another spot, then we've cut off the reaction of liking or disliking which feeds the mental states, all the thoughts, like "I want that spot, they're in my spot." all the emotions, and everything else that come on top of it.
Having unpleasant Vedana is not a problem, just like when I hold the fire, the unpleasant Vedana is not a problem either. It just automatically comes up, it will automatically come up, we can't stop Vedana arising. We can work towards changing how it will be in the future but we can't stop it arising. So if you understand that they always come up prior to the reaction of doing something, of saying something, acting something out, having anger, having desire, if you can understand that there's always a Vedana first, then you're in a better position to guard your reaction to things.
Then there is the second part discussing Vedana concerning body and mind. This is another area of frequent debate within Buddhism, because in English we use the word "feeling" for Vedana. Feeling can also mean emotions, which are mental, feelings in English can mean physical feelings such as heat and cold, poking, pinching, etc. Rosemary and I understand the word Vedana as only mental, only a mental reaction in the mind. That if you feel a poking on the skin, that's just sensation, that's not Vedana. The immediate mental pleasant or unpleasantness of the sensation on your skin, that's your Vedana.
Have your loved one stroke your arm, it's pleasant; do it for four hours, it's unpleasant. The thought changes but it is all due to a contact. So we feel that there is no such thing as a physical Vedana. It is always a reaction in the mind, it is a going towards a liking, it's a going away and not liking, or it is just neutral, it doesn't care. So the word "feeling" in English actually describes two or three different things, and this is a problem for the word Vedana in English, but it is the best word we can use or the best word we know to use, yet it also implies other things which are not Vedana.
So mindfulness of the body, if you are aware of sensations in your body, that's mindfulness of the body. If while you are observing sensations in the body you have a feeling of "it's hurting" and we start not to like the sensation, then that's a mental unpleasant Vedana towards the sensation. If we can just observe the sensation, we see that there is a bit of poking, squeezing or whatever, we go back to the breath, etc., then we are having equanimity towards the physical sensation. So that would be a neutral Vedana. If we have a physical sensation which feels very pleasant while we're doing the meditation, and we think "Ooh, nice!", then that's a pleasant Vedana in the mind due to a physical pleasant feeling in the body.