Here are my 6 tips on taking photos of insects and other small creatures with your smartphone, based on my experience taking HUNDREDS of blurry and unidentifiable photos.
1. The Full Picture
As best as you can, when photographing insects, try to get at least one shot of the entire creature, including antennae if they are very long.
Although close-ups of a particular feature can make for interesting photographs, they are often very difficult to identify. I like to try and get at least two angles: a "birds-eye view" shot, and one showing the creature from the side or underneath.
One way I like to do this is when I spot a moth on our glass doors. I get a photo of the underside from inside, then I creep around to the outside to get a shot of the upper-side. Having the underside photo can often aid ID.
2. Getting the Focus
One of the most frustrating things when trying to get a photo of a tiny bug is getting it in sharp focus.
For example, if you are trying to photograph an insect sitting on a flower, it can be hard to get your phone to focus on a small object in the foreground. If you can, without disturbing it, carefully move your hand behind the insect to give your phone a larger target to focus on. Some people carry a piece of white or blue card for this purpose (I am never that organised). Sometimes it is possible to use your hand as the focal point, then quickly take it away and snap the photo without your phone focus readjusting.
3. Know Your Limits
You will find there is a point when you get so close to your subject that your phone can't focus anymore. This is because you're getting closer to the subject than the phone's focal length allows. No matter how hard you try, the bug is still blurry - in this case, back it up. You can take the photo from further away and crop it down later.
One way to improve the focal length and magnification of your phone is to use a lens. I use a clip-on 15x lens, ordered online. However, before I had that, I found you could take decent photographs with a handheld magnifying lens. This takes some patience but the results are worth it.
4. Slow It Down
Sometimes, you just can't get a good shot because your subject is TOO FAST. Target insects when they are not moving too much e.g. while basking in the sun, feeding, mating etc. Sit and observe behaviour for a moment so you get to know when to take the shot.
Another way to get shots of an insect that is moving too fast is to use the burst shot function. This produces clearer photos than taking a video and pulling a single frame out, as videos are often compressed and lose sharpness.
5. Location, location, location
I always feel irritated when I neglect to record where I took a photo. Location is so important when identifying insects, and getting the most accurate location possible will really help your chances of getting an ID. In most phones you can turn on geotagging for photographs, otherwise, be sure to keep detailed notes on where you were.
6. Fix it in Post
I never used to put any effort into editing my photos after I took them. If you are also no Photoshop-wiz, at least consider these three edits:
CROP: So you saw a butterfly, but could only get so close before it flew off. You think someone could still identify it, but it's in the upper right corner of the photo and not very obvious. This is when you should use the crop tool: even if the image loses some detail from being enlarged, it helps the IDers see what it is you want IDed and saves them from having to zoom aaaaall the way in.
ROTATE: I like to rotate my moths so that their head is at the top of the picture. This just helps when comparing your photo to documented specimens, which are almost always photographed with the head at the top. For butterflies, I rotate so that the forewing is at the top, and the hindwing at the bottom. You may also like to do this for other insects such as beetles.
BRIGHTEN: Sometimes you see an interesting insect but it's just too dark, and flash is not helping. You can slightly adjust the brightness later to help highlight patterns that weren't obvious before.