A philosophical razor is a principle or rule of thumb that allows one to eliminate or "shave off" unlikely explanations or unnecessary actions. Think of them as shortcuts and ways to better interact with people and the world around you. Honestly, you've probably used some of these and maybe didn't even know there was a name for it!
"If something cannot be settled by experiment or observation, then it is not worthy of debate." This one is also known as Newton's flaming laser sword as named by Mike Alder. This says you should only focus on the problem through a combination of experimentation and reasoning, not argumentation alone. And if it's possible to perform the experiment, you should, as you cannot arrive at reliable truths by pure reason. Granted, they're a lot of things that you cannot experiment upon (history, politics, ethics, etc) so this one should be used cautiously and in very specific contexts.
"As a principle of parsimony, conversational implications are to be preferred over semantic context for linguistic explanations." Whoa, that's a mouthful!! More simply, address what the speaker meant, not the literal words that were used. People aren't always good communicators so give them the benefit of the doubt! When you focus just on the literals, you're being argumentative. Rather you should ask yourself, what questions can I ask to clarify?
"Never attribute to malice that which can be adequately explained by neglect." I've also heard it end with stupidity or laziness rather than neglect but the concept is the same. People are careless, unaware, ignorant, oblivious, etc. rather than truly evil. Most of the time people's behaviors have very little, if anything, to do with you. If it's clear someone is trying to hurt you and you've validated that, protect yourself (most likely you should just put distance between you).
"What ought to be cannot be deduced from what is." Or "A judgmental conclusion cannot be inferred based on purely descriptive factual statements." So the causes must be sufficiently able to produce the outcomes observed. If it doesn't, we have to either eliminate the cause as possible or add to the outcome to create the effect. It's not reasonable that a gust of wind made an airplane crash so you have to search for another factor in the equation.
"Among competing hypotheses, the one with the fewest assumptions should be selected." This is probably one of the best-known. Start simple, with the least assumptions, as the most likely. The reason is that for each assumption you add, you multiply the potential that you're wrong - it's not just double the likelihood that you've erred. For example, it's likely that raccoons got into your trash and made a mess rather than a homeless person looking for drugs when you live on 10 acres of land.
Hopefully keeping these in mind will help you as you navigate conversations and situations to make sure you're thinking as clearly as possible. To help embed them a little better, try coming up with your own examples for each of them!