People often ask this question. Of course, we all want to simplify the process. The truth is that real estate is all about negotiation, and there is no one rule.
First, you want to have seen a variety of homes in the area. When you find one that is right for you, ask a Realtor to prepare a "CMA" comparative market analysis" This shows at least 3 similar homes in the area and what they sold for. The sales must be recent, preferably within the last 6 months. You might want to drive by the homes that are listed as "comparable" to be sure there are no hidden factors such as a bad location or a really pretty lot.
Second, what's it worth to YOU? Does it have a special feature that the others you saw don't? Do you anticipate that you will need to spend additional money shortly after you move in? Make an offer in line with your budget, and don't go over your budget without a compelling reason.