Hey, huntrp27, glad you're going to try the repair. I've got some more details and pictures to hopefully help out.
First off, you'll need a couple of tools. I assume you've got a soldering iron of some sort, if you already got the replacement relay. Also helpful is some de-soldering wick or a de-soldering bulb, but you might be able to get the old relay off without this. The other tool that's helpful is a Dremel tool with a cutting wheel, or something similar. You'll need something like this to cut through the plastic housing that houses the two circuit boards that together make up the control board. OK, let's go!
First couple of pictures are the back and front of the Electronic Control Board (ECB). This is actually two separate circuit boards, back to back, inside a plastic housing.
Here's a picture of the "back" of the ECB, showing the circuit board containing the relays, etc. You can see the silicone potting material has already been removed from around the relays, and you'll need to do this in order to remove the bad relay to the drain pump circuit:

I used a heavy wooden skewer, but you also could use a sharpened wooden dowel or pencil. Something sturdy enough to push thru the silicone, but not hard enough to scratch the board.
Here's the "front" of the ECB, containing the other circuit board housing the display and the wash cycle selector. This is the board you'll need to remove in order to gain access to the back of the circuit board containing the relays. There are just three bendable tabs on the top of the housing holding this board, depress them one at a time and they'll release the circuit board. Remove this board with the display, and set it aside for now:
Now, here's a more detailed picture of the relay section of the "back" circuit board; the silicone has been removed, and you can see the 5th relay from the left is clearly labeled "Drain Pump". Once you have removed the silicone from around this area with your stick/dowel, measure the area's location within the housing, and "transfer" these measurements to the reverse side, where the display board was removed, which should now just be the plastic housing:
Once you have the measurements made for the area you need to cut away to provide access to the relay area on the "back" board, use a Dremel tool with a cutting blade (or something similar) to cut just through the thickness of the housing. You have some room to spare here, since there is also a layer of silicone between the housing and the solder joints on the back board, but take this part slow. Once you have the area's perimeter cut away, use the dowel or a screwdriver, etc to pry the cut section of housing away from the silicone potting material lying under the "back" circuit board. This photo shows what mine looks like:
We're getting close now. Remove the silicone potting material from the "back" board you exposed, using the skewer/dowel. Now you'll need the soldering iron and de-soldering wick (if you have it) to heat up the four connections holding the relay in place. This close-up of the first relay's solder joints shows the four joints which have been de-soldered; you'll need to do the same for the relay you remove (remember, you'll be removing the 5th relay. I removed the first relay on this "spare" board to use as the replacement relay for my washer's drain pump):
Assuming you've made it this far, what you need to do now is solder your replacement relay back into that same slot. Then pop the display board back into the front of the ECB housing, replace any ribbon cable connectors you removed earlier, re-install the ECB in the washer (making sure you reconnect all ribbon cable connectors previously removed to enable removal of the ECB. And that's it! Assuming the issue was the bad relay, you should have a working washing machine again. You can either try putting the washer into the test function for the drain motor (you should be able to Google this to find the correct button sequence), or just partially fill the washer with water, and manually advance the control until it starts draining, to test. Good luck, and let me know how you do! Also feel free to ask more questions if you have them.