Yes, you can install it yourself. It's really simple, just make sure you are properly grounded, i.e, absent of static electricity. The best way to do this is to wear an anti-static wrist wrap. But since most people don't have them lying around, the next best thing to do is touch some metal (not inside the computer) to discharge any build up static electricity within your body before handling the memory chip and never touch the metalic contacts on the memory card or internal parts of the computer and you'll be fine.
I've installed over 100 memory chips using that method and never had a problem (either I live dangerously, or get asked to do stuff for people at odd moments... at a party "oh by the way, could you install this chips for me", at a hotspot.. you get the picture) Again, you'll be fine.
Your system only supports a limited amount of RAM,
though there might be a BIOS upgrade available to install a higher amount (haven't checked, I'll leave the googling to you).
Here's links to the type of chip (you may find it cheaper at egghead or another spot) you'll need and a online manual showing the location of the chip and how to access it. It's really simple. Good luck.Memory Chip Armada 1750Compaq Armada 1750 - Laptop Upgrade, Disassembly & Repair