Why are all my games lagging?

Hard to tell from the minimal info you've given but I'd hazard a guess that the CPU is holding you back.
Of course you could have a ton of crud on your hard drive or way too many background programs running or any of several dozen other different scenarios.

Whats the model of the processor, what kind of hard disk do you have, what kind of PSU are you using, what resolution are you playing and what operative system are you using?

sometimes power supplys can be an issue if there isnt enough power to the unit. what is your PSU's wattage. and it is possible that pentium is bottlnecking dpending on what game you are playing. more details please certain games only need 2 cores where as some need 3 or 4 like battlefield 3 to run smoothly. since yours is a dual core thay may be problem. plus its a low clocked for todays standards. There are some basic fixes as opposed to upgrading hardware. close all background programs. its possible you have a virus. simple things you wouldnt even think of. like maybe your hDD is crammed and has a slow RPM. tell us your full system specs please

My Pentium Dual Core is E5300 2.66 ghz
My PSU is 350W

So which should I upgrade first?

Both...
http://www.amd.com/US/PRODUCTS/DESKTOP/GRAPHICS/AMD-RAD...
Read the power supply recommendation.

Does your power supply even have the 6pin power connectors for the video card? Wouldn't surprise me if your card isn't getting enough power so it's remaining in 2d clock speeds, that would cause severe lag in just about any game. 350W isn't enough for a card like that, especially if its a cheap low end no name power supply.

He's probably using the floppy-drive to video card adapter.

Yep, need a CPU+power supply upgrade as a minimum.

EDIT: You'll get lots of opinions here, but I'd probably get at least a core2quad if your mobo supports it. For a power supply, get a 650W+ model by someone name brand. Like Antec, Corsair, OCZ, XFX, etc. You should get at least a 3-year warranty on any decent model. Upgrade the power supply first if you can only afford one right now. If you upgrade your CPU first, you could smoke your old power supply and/or your PC with that low wattage...  

Wow no wonder you are having trouble. your power supply is probably at maximum usage or close to it. i would go with power supply first cuz that may blow out soon  . then worry about the CPU as it wont be your main problem for older games. go with this
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
be careful when replacing a PSU for your first time seek advice 

My PSU has a 6pin connector

It has 6 pin connectors

Even if it has them it doesn't mean it puts out enough power, a 350w (even the very good ones) can only put out say 250-275watts max (and you should never ever run a psu near the limit) the 6850 alone uses 130watts, and your cpu uses 75-125w
hard drives are about 5-10 watts each as are dvd drives, and fans are about 1-5 watts each

so basically, just get a new psu.

Ah ok, we were a bit doubtful on a 350W supply. Most of these smaller supplies are used in PCs that use power off the PCIe bus, so you don't need an external connector.

@theitaliansico,

I have a Corsair supply myself & it's a tank...this one looks pretty good too at Newegg and it's a little cheaper if the author is on a smaller budget:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

EDIT: Note that you only get a 3-year warranty on the OCZ vs. the 5-year corsair, however.

I personally use this one: http://www.newegg.com/Product/Product.aspx?Item=N82E168...