I'm sympathetic to this because, sadly, there are places who only realize your value when you're with someone else, and then forget all over again once you're back. The thing is, not all companies think this way and I would generally advise to try and migrate towards the ones who appreciate your service while, you know, you're actually there.
That being said, there are lots of other factors that might make you want to return and so I think that being relatively straightforward is fine. To that end...
Don't outright talk trash about the company unless you absolutely do not want to come back until Thing X is replaced, and even then you may want to keep that to yourself. If you didn't get along with your boss, unless that boss is running rampant you're probably better off not saying anything and then, down the line if they want to rehire you, determine at that point who you'd be reporting to and make your decision then.
Speak in terms of "I" rather than "you" statements. "I am moving on because the new employer is willing to pay me at a rate that's about what the average person in my position in the industry is making" instead of "you guys aren't paying me enough".
Prepare to be counter-offered if you do name specifics. If you are leaving to become a lead at another place for 10% more money, you should at least be prepared for the possibility that this company will offer you the same thing. They might not, but if you still want to just get out - which is not necessarily a bad thing; if you have to go out and find a job every time you want a raise, that can get very tiring very quickly - just make sure you've got a response prepared for that.
Some companies/owners/HR departments weirdly take it super-personally when you leave for a similar position at another company. If you want to ever consider going back, consider those eggshells that you have to walk on.