The first op amp sets up a reference at Vcc/2 for single supply operation. The resistors on the input limit current to the body and set up a body reference at or near the common mode voltage on the electrodes (using big noisy resistors). The instrumentation amp takes the differential signal, provides a gain of 5, and spits it out as a single-ended output, where the next op amp low-pass filters it, and then sends it to an inverting amp with a big gain (1M/3.3k) that also removes most of the DC offset prior to amplification.
I'm almost afraid to tackle this one, but here goes.
Stop. Just stop. Forget EKGs. Get a cheap DMM, find a web page that deals with really simple op amp circuits, and start building really basic stuff, like a voltage follower, then a non-inverting amp with a gain of 2, and work up from there. The LM358 data sheet has some very basic circuits that you can try. At this point there is simply no way help you "fix" what you've done. Your schematic makes no sense at all, and the Fritzing does not correspond to the schematic.
In the schematic, there is no pin connected appropriately. Not one. First, you show an OP37, then you say you don't actually have an OP37, you have an LM358. Why did you do this? You have +5 going to the V- input, and D9 going to the V+. The LM358 doesn't have trim inputs, and on the OP37 that's not how to connect them. And the output doesn't go anywhere. Finally, an op amp is not run "open-loop" - that is, without feedback from the output to at least one of the inputs. So just running your signals directly into the inputs is not going to work. Like I say, there is not a single pin connected appropriately.
The Fritzing shows, for instance, +5 connected to pins 4,5,7 and back to DIN. There is no ground connection to the breadboard, so there is no ground connection to the op amp.
I'm sorry, but when you're this far off, there's no easy place to start.
Cease with the EKG for now. Concentrate on making a few simple circuits that work, and only then move on to something more complicated.
Best Answer
Without looking at your circuit (unless you post a schematic), at least your parts seem right. Personally, I'd recommend the AD623 over the INA333 (of course, I don't actually know your specs, so take w/ grain of salt) simply because the inputs on the 623 can actually go a tad BELOW the low rail, which is a huge benefit.
The way to achieve what you're trying to do is an instrum. amp. stage with V+ as 5V, V- as ground, and Vref as 2.5V. You'll need to buffer the 2.5V before putting it in to Vref. A voltage follower there is pretty standard. The Instr. amp. should have a modest gain of about 10, to avoid saturating on differences in electrode skin potentials. The inputs of the amp will go to the two ECG leads, and the ground can go to the leg lead.
After the input stage, you want to filter with a low-freq cutoff of about 0.1Hz and a high-freq cutoff of about 110Hz, and then an amplifier stage w/ a gain of about 150. You can build your low-pass into your amp stage, but you should hig-pass before you amplify.