Actually, another way (with zero contamination risk) is to measure the fermenting beer temperature. Even something as inaccurate as one of the fermometers will help. Depending on how low you chilled the wort before pitching, and if it's below ambient temp, then you'll see the fermometer/thermometer show an increase above that indicating yeast activity inside (generating heat)...
Personally, I have a thermowell going into my fermenters, so that I have an easy way to get a temperature reading. The thermometer unit records high, low and shows current. This allows me to see when it's peaked and is on the drop as well. I also don't take a gravity reading after pitching the yeast until it's gone to the keg. I've used the same few strains of yeast enough times to know when they're done. Plus, I give them enough time to be done without question.
Since this is your first, a few gems to help...
1. Ignore time frames on the kit/recipe instructions when it comes to time fermenting. The yeast will work at it's own pace and humans have no rights to interrupt their work.
2. You don't need to rack to another vessel for the vast majority of brews. Basically, if you're making something with ale yeast, you can leave it in primary for the duration.
3. When it's done fermenting, and you're trying to figure out if it's time to bottle/keg it, pull a sample, take a gravity reading and TASTE it... Repeat 3-7 days later and you'll know if it really is done fermenting and IF it's ready to keg/bottle. If you detect any off flavors, give it more time right where it is.
4. More time can cure almost all issues with a brew. Only a few things cannot be fixed this way. Included are oxidation (each time you rack the brew, chances of that happening increases), infection (opening the fermenter too long will increase that risk, as well as not using proper sanitation practices) and issues due to water chemistry.
5. If you're not already, get some no-rinse sanitizer like StarSan and DON'T use something chlorine/bleach based.
There's more, which can be found just by cruising the boards or using the search tool.