How can I tell if this is something I can fix before I call in a repair person?
Do you know where the leak is coming from? And what needs to be replaced?
If so…you tube!
Or are you asking how to figure out if you should even call a repair person?
I was hoping I could figure out if it is worth it to call a repair person.
I watched a couple of youtubes after posting this. It looks easy to take it apart far enough to see if I can find where the leak is coming from. Or maybe I can just have Happykid tip it over a bit so I can check the tubing for drips.
I moved the dryer so I could get closer to the washer, and found that the tube that connects to the vent on the outside of the house has broken at the dryer-end, leaving about an inch and a half of lint all over the floor back there. So we do get a trip to Home Depot for sure tomorrow. 
I don’t know…for leaks…I would call a repair person.
Is this a high end washer? Sometimes they just aren’t worth fixing these days…
Its a kenmore that was new when the house was flipped in 2007/2008. I shut off the water last night, and it still is leaking. That tells me it is time to call the repair person. Probably just a hose, but maybe something else. There are basic Amana models at Home Depot for about $500. That’s enough washer for us if the repair is too serious.
To determine the source of the leak, try the paper towel trick. A paper towel like Bounty, or with some ridges/bumps on it, when it gets wet, the bumps will disappear forever. So wrap them around the input hose, and you can find out if the hose is leaking.
Replacing an input hose is a piece of cake - these should be replaced frequently anyway.
If it is not the input hose, it might be the pump. Taking the machine apart, and then while running it, you should be able to identify where the water is coming from.
It could also be the discharge hose. See step 1.
Depending on the model, it could be a valve on your cycle switch. These are easy to replace, watch youtube videos, but you can’t always get the parts.
With a 10 yr old machine, you should still be able to find a replacement pump - order it online, and it should be fairly cheap (under $75).
Hiring a repair person makes the investment typically $150 more - at which point you’re a nice chunk towards downpayment on a new machine.
But it is satisfying to do it yourself, and save the $$$.
Parts Select has helped us repair many appliances and have great u tube tutorials.
Installed the new dryer vent single-handed today. I feel so good about that, and soooooo dusty! It really should have been a two-person job but oh well.
While I was down there, I realized that since the drip is not ginormous (not dripping at all today with the water turned off), I don’t have to fix the washer just yet. I have time to do a bit more research and maybe charm my not-so-handy spouse into helping me with this.
@oregon101 thanks for the Parts Select information!
Is it the washer or the plumbing leading to or from the washer?
Pretty sure that it is the washer. The plumbing entering and leaving the machine is bone dry. In some, but not all, wash cycles a small drool of water appears around the lower right hand corner of the washer. It is in the basement on cement, so no worries about wrecking the floor.
Sounds like a pump to me, perhaps it has a hairline crack in it. This happened to MIL’s machine, and was very easy to replace (my DH is not afraid of these things). He said they put plastic pumps in nowadays, and they don’t last, especially if you have a well and have any mineral content in your water (we have high calcium in our area). I am always pleased that DH is so handy. Sure, it would be probably have taken a pro about 15 min to replace what took DH an hour, but they would have charged at least an hour’s labor to come out.
Get your make/model number and look online for pump. Remove the old one and inspect it - you probably can see the crack, or even watch it drip once you remove the back cover.