There is a list of steps here.
According to that page, here are the places, going in order, that you should look for the radical:
1. The entire character
If the entire character is a radical, then... well, that's the radical. Examples are 人 and 火. Also, if the character only contains one radical (not listed in one of the 214 Kangxi radicals), then obviously that is as well.
Anything covering 2-4 sides of the character. Examples are 气, 凵, or 囗.
Radicals on the left of the compound, but not underneath anything (e.g. 言 in 罰 does not count). There are tons of possible radicals here, but the left parts of 忙, 休, and 私 are some examples.
Same as above, but on the right. Examples include the right parts of 次 and 部.
Grass (艹) and roof (宀) are very common examples, in characters like 花 and 守. Note that it has to be covering the entire rest of the character, so something like grass in 描 doesn't count; the mountain in 崩 counts because it's entirely covering everything else.
If the top part is complex, it may be the bottom. 力 in 勢 is an example; so is 木 in 楽 and 示 in 禁.
7. Top Left
Now we're getting a little desperate. If the entire character is split into a left piece and a right piece, but neither is a radical, then try the upper part of the left half. For example, the radical of 執 turns out to be 土.
8. Top right
If it's not in the top left, then try the top right. For example, 目 is the radical of 県.
9. Bottom right
The mouth in 君 is in the bottom right, I guess.
10. Bottom left
I can't even find any examples other than what the site I linked gave, even among non-jouyou kanji. The bottom part of 虱 is the radical (because the enclosing part isn't actually a radical), and 米 in 糶.
11. Somewhere else
There always has to be a catch-all, right? For example, 言 is the radical in 讎.
There are probably exceptions, or cases where it's hard to tell/borderline (in fact, a few examples I gave probably fall into that category). In the worst case scenario, you can at least narrow it down to two or so options and then try both.