Fitting component group set to bike
As you mention upgrading to 105 I assume you are looking to upgrade the groupset only. If you want to upgrade wheels and other things as well you'd probably be better off selling the bike and buying a new one with the components you want.

Bicycle groupset components are extensively standardized so there are only a few things you need to know to ensure compatibility. On a rim-brake road bike it's even simpler that more modern hydraulic disc brake bikes. Basically you can just order a 105 version of each groupset component you have now. Shimano helpfully provides extensive documentation, the easiest way to look at the various options in a grouset and to see which components are compatible which each other is to look at the Line-Up pages. Here's the one for the latest 105.

However, there is a issue with upgrading to 11 speed 105. I'm assuming this is the bike that is equipped with a 9 speed Sora groupset. The rear wheel likely has a 10 speed and below compatible hub rather than a 11 speed compatible hub. The splined freehub body that the cassette slides onto is 1.85mm wider on an 11 speed hub. If your current cassette has a ~1.85mm spacer behind it you have a 11 speed hub.

If you don't have aa 11 speed hub you have a couple of choices: go for 10 speed Tiagra, buy a new rear wheel or make a 11 speed system work on a 10 speed hub. Some 11 speed cassettes will fit on a 10/9/8 speed hub, but they are all wider range ones with large inner sprockets. The Shimano 105 GS long cage derailleur will accommodate an 11-34 cassette (officially, many people say it will work with a 11-36). I'm not sure which 11 speed Shimano cassettes fit on a 10 speed hub so you are going this route you'll need to do some extra research.

If your bike has an FSA crank the bottom bracket will need to be updated along with the crank. If you have a '2-piece' Sora crank with the axle attached to the drive side crank and external bottom bracket cups threaded into the frame the 105 crank will fit in the bottom bracket cups, although of course you may choose to upgrade the bottom bracket anyway. I'm not sure if older Sora cranks had a '3-piece' type with a cassette type bottom bracket, if you have one of these you'll need to upgrade to 105 external bottom bracket cups.

For the Trek One Series you need rim brakes obviously, you want the 'dual pivot' style not direct mount. You'll need to determine if you need a 'band clamp' front derailleur that clamps on the seat tube or 'braze-on' that attaches to a lug on the seat tube (these lugs were brazed on on steel bike frames, hence the name).

The other choices are crank ring sizes and cassette range. If you are a beginner you'll probably want a lower range 'compact' 50/34 crank. If you live where there are hills you'll want a wider range cassette and long cage GS derailleur. 

If you are installing all the components yourself there are great resources online for learning how to wrench on a bike. Park Tool is the best IMHO. Also, Many online bike retailers offer groupset kits that include everything you need for an upgrade, that are cheaper than buying all the parts individually.