For the most part you can't ensure the correct components are present just by looking inside the case since so many different makes and models look alike. In addition, not all components have labels on them with the proper identification. Thus, the best approach is to take an inventory using a program such as Everest, which is freeware. It will analyze your PC, recording almost every component installed, along with the make, model, specs, and serial number, if applicable. Specifically, it will take care of the motherboard, processor, RAM, optical drives, hard drives, disk drives, graphics and sounds cards, and networking adapters. It will also note your keyboard, mouse, and monitor, just in case you're packing them up as well.
To get the ball rolling, install and launch Everest, then click the Report button along the top or go Report->Report Wizard. The "System Summary" should suffice, though you can choose to receive a full report if you prefer. Depending on which report type you choose the report could be quite long, so you may want to save the file to a flash drive instead of printing it.
Note, however, that this inventory is not quite comprehensive, for not all components are capable of reporting themselves via software. These items include the power supply (PSU), fans, and the case itself. The latter should be easy to identify and the fans are of little consequence unless you purchased high-quality parts, leaving you with the PSU. If you peek inside your case you should find it in the top back region of the case with a large label stating the brand, model number, and wattage. Write those down for later references.
Once you receive your computer back from the repair shop, you can repeat this process, comparing the initial report to the new one. Any components you had them install should be properly identified on the new report, while the rest should match the old. If there is a discrepancy chances are something's not kosher.
Some other things to keep in mind:
* If there is a software issue the repair shop may reinstall Windows without your permission, wiping out all of your personal files. Thus, it's always a good idea to backup what you can't afford to lose first.
* Likewise, if there are any personal/private files you don't want them to happen across, you may want to move them to a flash drive or other form of removable storage before boxing it up. They could still drudge it up off the hard drive, but it's a little added precaution.
* Always request a written work order before they perform any work on your computer, clearly stating what they will do and what they will charge. In addition, always request a receipt upon completion, stating what work was performed, what parts were added/replaced, how much was charged, and what warranties are given.
* If you are paying for the work to be done, as opposed to having it covered under a warranty, request that the old parts, if any, be returned to you. They are yours and you can always use or sell them later. In addition, if it turns out they replaced a supposedly defective part when it was indeed functional (some will report false problems just for the business) you can request a refund for the purchased part, though not necessarily the cost of labor.
* Be aware that some repair shops will try to 'do you a favor' by installing their own copy of Windows instead of your own or the one you purchased. This almost always results in licensing issues with Microsoft reporting your copy is invalid. Never be talked into such situations and be sure to call Microsoft's toll-free hotline if Windows suddenly begins telling you your copy is pirated afterwards.
And remember, even reputable repair shops, such as Best Buy's Geek Squad, have been known to perform shady practices, so never assume it'll be alright. A little caution can go a long way, particularly with an investment such as a computer.
Hope this helps,