The easiest way to slice a tomato is to throw it through a harp. To dice, do it twice.
Yeah, sorry, it’s a typo. Although I often use my finger as a finder, that is not its sole function. It is also a tomato de-pulper.
The only part of a tomato I generally remove is the tough green/pale part where the stalk was. I usually do this by cutting the tomato into quarters vertically and nicking off a little wedge at the top to get rid of the tough bit. Then I dice. I don’t usually care about the seeds, though if I am going to remove them and/or the skin, it’s extremely easy to do once the tomato’s in quarters: just slide your knife along like you would on a melon.
I agree with the knife being sharp being the most important thing, though. When I’m sharpening the knives, they’re sharp enough when just resting the weight of the blade on a tomato and pulling the knife towards me with no pressure leaves two half-tomatoes rocking on the board. No mushy tomatoes in this house!
My Super Secret Tip™ in regard to tomato pieces is to lay them on a paper towel to mop up the juice. I then roll them slightly to get most of the seeds. I’m not over-worried about seeds in my final product.
I use cherry/ grape tomatoes all winter to make salsas and pico de gallo type stuff, and it works particularly well with them.
One test of a sharp knife is that it should be able to slice through a tomato using only the weight of the blade. If you have a knife this sharp, dicing a tomato is no problem.