How can I do alternate exercises between days for best results?

Great question. I alternate between free-weight lifting on even numbered days and heavyhands aerobic workouts on odd numbered. I’m up to the maximum 15 pound weights for the heavyhands.

You can do heavyhands every day, so on the months that end in 31 and are immediately followed bu a 1, I have no problem. It makes it much easier to keep up with which exercise to do than the every other day approach. All I have to do is look at the calendar/clock on the computer monitor, and I immediately know which exercise to do that day.

you can do heavy workouts on major muscle groups everyday. Other musclegroups you need to allow them to rest a day. Heavy workouts on a muscle is tearing the muscle fiber, thus making it bigger and adding to the strength. You need to let it have a rest to heal at least skipping a day. If you are properly isolating each muscle, you have plenty to go around to keep you busy.
If you dont have one, it is helpful to have a muscle anatomy diagram to also help you identify the musscles so you can create a program to focus on what your body needs.
It certainly takes time, but with dedication you will see the differences.
Certainly add an aerobic workout of at least 30–40 minutes reaching 60–80% target heart rate into your routine. Along with the right nutrition to refuel you and you will be able to attain your goals. As always, know when you body is asking for a rest. You can overwork and that can be more harmful as it can ruin the flow of what you have going.
A tracking sheet is helpful as well, but after awhile, you will know and feel where you are at.

Will weighted push-ups, for example, help me increase weight or reps on DB press?

Mixing up the exercises is a good thing. It is like what weight lifting is meant to do, and that is to simulate hard physical labor. Adding aerobic exercises to your routine will also help with this simulation. Other things, such as isometric exercises can be done at any time too. While at work, in the car, anywhere. It will ‘trick’ your body into thinking you are a hard workin’ rock liftin’ hunk of muscles.

I’m trying to change my workout every day… I do DVDs at home which enables me to do this. I do dancing, step, boxing, weights, toning and general aerobic exercises too. I think this gives you an all round toned body and helps to keep things interesting and fresh… Furthermore…I’m constantly surprised how some high impact exercise like dance routines can be such a different challenge than say simple jumping jacks… You’d think you’d have the same cardiovasuclar strength but all the different combinations of muscles groups targets such a variety of areas that I think a varied exercise routine is the best….

I’ve also heard about what @blueiiznh said about muscles fibres tearing so I try to gives my muscles a little rest if they feel sore…time to heal and get stronger.