Let's take the example of a single keyword, which we aren't sure how it'll perform.
We'll need to make a few more assumptions to get started. Hopefully, you can produce these based on similar activity in the account, or on your site.
You'll need an Average Order Value assumption first. If you're targeting a specific product, that product's price is a reasonable place to start. We'll assume $150.
You'll also need a Conversion Rate. You can either use data from a similar campaign, or your site's average. Don't worry--it can be a ballpark, as this will correct course quickly enough. We'll assume 3%.
You'll need to know how much you're willing to pay for advertising, as a percent of revenue. Too high, and your margin erodes. Too low, and you give up market share. This figure is called your Cost Of Sale (COS), and is just the reciprocal of your ROI target. Let's assume you're looking to spend no more than 15% of revenue for these ads.
Now, with the COS and the AOV, you can arrive at a Cost Per Acquisition (CPA) target. This is how many dollars you can spend per conversion. In our case, it's $150 * 15% = $22.50. That's how much we can spend to generate the clicks it takes to produce a conversion.
If we have the Conversion Rate, then we know how many clicks (on average) that takes. At 3% conversion rate, we average an order for every ~33 clicks, so the $22.50 is all we can pay for them and still hit our goal. That's $0.68 per click, and that makes for a GREAT starting point.
But how do you know when to give up? You can use Wolfram|Alpha to find out how many clicks it would take to get to 95% probability of a conversion:
The .03 is our conversion rate, and the .95 is the certainty we'd like to hit. This solves to ~98 clicks, so we'll run our test to at least that many.
If you get a conversion sooner than that (with some sort of upper bound), you can bid based on the real conversion rate. For example, if you got a conversion after 25 clicks, you can bid using that 4% number. If that's actually too high, you'll have collected the additional clicks to know that fairly quickly, so it turns itself back down before it spends very much. If you aren't getting a conversion, you can also bid as if you had only one. If you are at 90 clicks, for example, and still haven't seen a conversion, you could bid as if you had one, bid using the 1.11% rate, and your bid will be cautious, skeptical even, and your spend will be controlled.
Now, this was all for a single biddable entity, perhaps a keyword. What I'd recommend is to keep your long-tail keywords separate from your higher-action keywords, in different AdGroups. As you sift out higher-performers, move them to the main group. Slower-action keywords can stay in the long-tail. You may not even need to bid at the keyword level, if you use this strategy, as you can apply exactly the same logic to the AdGroup level. If the entire Group is a new test, then this will accumulate clicks more rapidly, and reduce costs.
Now, how ever broad you go will set how much risk you're taking on. If you have one keyword, like this example, you're probably only going to spend about $50. If you do that thousands of times, then that number goes up with it.
If you'd like to talk through this, I'd be happy to do so. My VIP link is: https://clarity.fm/roysteves/statbid
Each keyword has a different search volume and level of competition, and prices are highly impacted by those numbers. So before knowing how to bid, it is important to look at the keyword you are bidding on.
Even long tail keywords can be competitive, and a number of situations can play out.
Maybe you need to bid above the recommendation because you want to fight for visibility. Maybe you want to bid 50% less just to test the waters and see where it gets you.
No matter what you decide to do, be prepared to learn and react.