I have owned 4 Notebook PCs and FYI upgrading RAM to the maximum is limited or restricted by the manufacturer installed Motherboard. It is true that every Notebook PC I have worked on normally only has 2 memory module slots and if your Sony has 1 GB from the factory, then it's probably older like my DELL Latitude D800 that is Intel Pentium 1.7M Centrino with two 512MB memory modules (1GB total). Before I would even be able to think about upgrading it, may I recommend you visiting CRUCIAL MEMORY bec it is the best starting point for all RAM memory upgrades for PCs bec they have all manufacturers and models, the website will also tell you the maximum memory for that particular motherboard, it will give you a good idea of your maximum out-of-pocket costs for QUALITY RAM parts that is GUARANTEED to be COMPATIBLE. By the way, the bad news is that your existing two 512MB memory modules cannot be installed elsewhere and if you're lucky you might be able to sell them on EBAY or Craigslist but probably could not recover or reduce much of your out of pocket costs for new, more powerful CRUCIAL memory
Installation of Laptop/Notebook memory in most cases is fairly simple job, the "touch and go cross your fingers" ordeal normally will be rebooting your Sony Notebook with upgraded memory where visiting SYSTEM in the Control Panel, one can always read how much RAM, Windows XP recognizes.
I have 2 newer DELL Notebook PCs where I paid Dell extra for the VISTA Upgrade CDs but for example, my E1505/6400 Inspiron came with 1 GB memory and I went on EBAY and bought genuine DELL matching part numbers carefully to bring it up to the maximum 2GB. In the case of my wife's new Dell Latitude D620, it came with only one 512MB module, but it is a business grade PC that will accept up to 4GB memory total but bec of VIsta upgrade eventually I wanted it to have at least 2GB memory. Note that installing one memory was out in the open on the bottom via a panel door with screws, but the second memory module was a bit more tricky and actually requiring removing the keyboard.
In the event you reach the conclusion that maybe a new Notebook PC is your best solution then I would seriously think about visting the DELL Outlet bec those Notebook PCs have at least full one year warranty and upgrade/replacement parts are readily available and reasonably priced thanks to Dell's larger than average number of PCs in the marketplace since majority of businesses use Dell. Dells are quality built and can last a long time!
Some Lessons Learned: (1) MEMORY at a minimum you want is 512MB and 1GB is better and 2GB even nicer. I paid over $1000 for my 1st Gateway Pentium IV Notebook and for the longest time was unhappy bec I never realized 256MB was reason why so slow on internet. Luckily I found the compatible 256MB to upgrade. (2) Size of BATTERY can be key esp when taking to lecture classes etc or in bookstore/library. (3) Wireless WiFi Internal Card is absolute must (4) Get the biggest Hard Disk you can afford and don't settle for anything smaller than 60GB. (4) CPU if buying new Intel Duo Core should be fast enough but if buying used, then I would recommend Pentium M Centrino as your minimum and never waste your money on Pentium III no matter how cheap bec you will be disappointed buying something worthless that might give you trouble trying to unload.
Best of Luck!