How can the Higgs boson have mass?

As you can imagine, this is a very technical issue and it is very difficult to make good analogies at B level. Questions such as "how can A give B?" are by nature going to be best answered on a rechnical level, but you would first need to understand the framework and how it predicts things to work. Only then can you adequately get your question answered.

That being said, you are likely to have some sort of mental image of the process. In order to address that, you would have to be more specific on why you would not expect the Higgs to give mass to itself.

Also, in the end, it is not the Higgs boson which gives mass to other particles, it is the vacuum expectation value of the Higgs field which does. Making an analogy to a pond, the vacuum expectation value is the depth and the particles are ripples on the surface.

 

This is simply not how the subatomic world works. You cannot think of Higgs particles as little balls sticking to things and thereby giving them mass. And again, it is not the Higgs particle which gives mass to other particles, it is the vacuum expectation value.

 

No, like normal particles. All particles are essentially disturbances in their respective fields. What sets the Higgs field apart is that it can have a non-zero value in its lowest energy state. It is this non-zero value which results in giving mass to particles.