I will first look at the price to see if it is even near the range of what I usually like to pay (< $20) because unless the seller is feeling extremely generous, I've never negotiated more than a 40% discount. Once you get past the starting price, inspect the razor to make sure it is something that is at least salvageable. If the price and condition stipulations are met then you can being negotiating.
First ask the seller what they would take for it. Usually they will ask you what the tag says and then knock off a few bucks. Then you can counter offer "Ah that's a little out of my budget, will you take X.XX for it?". Your starting amount can't be so low that they think you're just trying to walk out without paying them but you should give enough room where they can counter and reach an amount between the two that you feel comfortable paying. Here's an example: Let's say it's a 5/8 heavy grind Sheffield razor with some rust spots on the spine and tang, but the manufacturer stamp is still intact (not a W&B hyped manufacturer) and the edge is clear of pitting. The scales are probably horn and have some bites out of them but aren't cracked. The price tag says $30. After asking for the price the seller knocks it down to $25. You counter with $17 because it does have some ugly rust, will need some experienced restoration on the scales, and to be repinned after being taken down. The seller offers an even $20 and you've just negotiated a 33% discount. I can honestly say this is how the vast majority of my completed sales have gone down at flea markets and individually owned antique stores. If the seller's counter ($20 example) is too high or they completely scoff at my offer, I will immediately say thank you and walk away.
As was mentioned before, antique malls where the item owner is not present (or may have given a 15% discount to all the items in their booth already) it will be very hard to negotiate. I have had instances where the antique mall owners called the booth owner to do a little haggling, but it usually didn't result in much of a discount. There will also definitely be times when you find someone who is a "collector" and not a "salesman", at which point, negotiation may result in a couple bucks off but they value their items much higher because of the intrinsic value it holds for them. Try not to deal with these people unless they have your holy grail of straight razors sitting in their cabinet in very good condition.
I also use the bulk discount tactic sometimes as long as the average price for all of the items comes out to something I am willing to pay for each. A $20 strop in dirty but uncut/nicked condition was discounted to $15 immediately. Throw in two razors originally priced at $16 for the pair, and suddenly the total price is $25. Wonky math right?
I find negotiating to be almost as fun as hunting for the shaving gear in the first place.