Lots of good advice here. Best to use a Realtor...know the comps...know the condition of the property, etc. And, as pointed out below, "low balling" won't necessarily get you the "best" deal. However, let me add a bit more to the mix.
You won't be absolutely able to determine the seller's bottom line, but in order to get the lowest price (which, as noted, may not be the "best" deal), you need to know as much as you can about the seller and his/her situation and motivation. So, in addition to the information presented below, find out what the seller paid for the condo. Now, he/she may have refinanced, but...if the seller paid $260,000 for the condo, it's fairly likely that that's the seller's bottom line, net, even if pretty seriously motivated. You build in the Realtor's commission, and there probably isn't too much seller wiggle room. On the other hand, if the seller paid $80,000 for the condo 10 years ago, then there's a lot more downside potential and a lower offer might be more readily accepted.
How eager is the seller to sell? Again, it's impossible to tell for sure. The agent representing the seller isn't supposed to reveal that sort of information unless the seller has authorized it. But it doesn't hurt to ask why the seller is selling. And that can reveal degree of motivation. "Well, he'd like a larger unit so he can have a computer room" is quite different from, "His company relocated, and now he's got a 2-hour commute each way, so he's looking for something closer to work." The more motivated the seller, the better deal you probably can cut.
Most agents will advise you not to offer too low a price because the seller may be insulted and won't even counter. That's true. On the other hand, investors have no problem making really low offers, knowing that most won't be accepted. I know you're not an investor, but if you're really looking for the best price, after taking all the advice here from everyone into consideration, make an offer that works for you.
Hope that helps.