Back in my 30's I trained a lot for the mile and did the 5k road race thing. As part of that, there were many 400s in my training schedule. I did a lot of them for time, but only rarely did I legitimately sprint, so I wouldn't worry about doing that for 400 meters. Think of this as a fast jog.
In my 40's I got tired of running longer distances and pretty much did sets of 400's a few times per week to stay in running shape.
Your main obstacle, is going to be taking it slow and not developing Achilles tendinitis or nagging shin splints. So stretch lightly before and after.
So to start, I would just do some alternating walks and jogs with your dog. Start with 15 second jog/1 minute walk a few times per week and slowly build the jog time to 1 min, taking at least one minute to rest over a couple of months. Then add days until you are doing this every day, or at least every day you walk your dog. Try to time your jogs with uphill inclines as this is speed work in disguise and is much easier on the joints.
This should get you started and you will be surprised at how much fitness you can gain doing just this little bit extra. After phase 1, you should be ready to jog 400 meters few times per week.
Others have mentioned actually doing sprint work over shorter distances as part your training. It works wonders, but I am hesitant to recommend it before you have been running for a couple of months. But if you do want to try it. Only do it once every 7-10 days.
My in my 50's sprint workout would look like this, and I am sure you could do something similar:
All sprints 100-150 meters (pick an approximate distance) MAX will be your fastest jog in the beginning. After about 6 weeks you should be able to get to 5min/mile pace in the middle sections.
Sprint 1: Jog to begin, accelerate to 50 % of max in the middle, decelerate towards the end.
Sprint 2: Repeat Sprint 1 with 60-75% of max in the middle
Sprint 3: Repeat Sprint 1 with 75%+ of max in the middle. Start a little faster and decelerate a little slower.
Sprint 4: Repeat Sprint 3 with 90% of max in the middle.
Sprint 5: Repeat Sprint 3 with 100% of max in the middle.
Sprint 6: Repeat Sprint 5.
Sprint 7: Repeat Sprint 3
Sprint 8: Repeat Sprint 2
If you do nothing but walk/jog with your dog and these sprint work outs, then you will need no other running specific training until about a month before the "race", where you can add in some weekly work outs where you will run 400 meters and walk 400 meters for 4 to 8 sets once per week just to get a feel for time, curves etc.
Your friend is horrible, you should win convincingly.