The 'simple progression' articles will be a series of blog entries giving examples of some of the most straightforward and effective ways to progress with basic training. This first method is primarily intended for beginners or intermediates using high repetition exercises--primarily bodyweight, but also kettlebells, or sandbags. Perhaps high repetition barbell lifting as well, though not many people do that (I'll have a post giving one useful example of that soon). Of course, more advanced athletes and lifters can use this first method as well, when in a deload or base building phase when more endurance is desired.
For a rank beginner, movement is most important. Or, to be more precise, making movement a daily habit. I don't train hard every day, but I believe it's important to be active on some level, every day or close to it, in order to be generally healthy. It's a cliched saying in training but I believe it holds for beginners nonetheless--if you are only active for 30 minutes each day, do you think your body will respond to those 30 minutes, or the 23 hours and 30 minutes you spend sitting in a chair behind a desk, on a couch, or lying in bed? The most important thing to do is not only begin activity, but maintain it, and force your body to adapt and 'realize' that it has physical demands to meet.
Thus, beginners should train every day. It won't be possible to make progress or even give a best effort every day, of course; (though beginners can certainly progress more quickly than more advanced trainees as their bodies rush to adapt to the new strains). So, a very basic rep cycling program can be easily implemented to make those first forced progressions a bit more efficient. Some days, you'll work harder and go for a new 'personal record', or PR. Others, you'll take it easy. These lighter sessions will help get some blood into your muscles and aid in recovery (some people call this 'feeder' work), and also keep you moving and doing something even on the days you can't go all-out.
Here's an example. Say you can do 30 pushups to begin with. You'll do one set each day.
Monday: 30 reps (all out effort)
Tuesday: 15 reps (very sore from the day before, but this wasn't too hard)
Wednesday: 20 reps (last one was only slightly challenging)
Thursday: 33 reps (struggled, but got a new PR!)
Friday: 25 reps (not as sore as after Monday's effort, so did a decent number)
Saturday: 15 reps (took it easy, did these with scarcely any effort)
Sunday: 35 reps (another PR)
If you want a percentage plan, 100-50-75-100+ is one simple way to program this, i.e. max out, do half the reps the next day, three-quarters of your best the day after that, and if you feel good on the next day, try to beat your original number.
Because you're doing only one set, recovery is fairly easy, and your body will adapt quickly, so gains will be rapid. Also, you should probably do several exercises one after the other if you want some conditioning/cardio benefits, because a single set won't do much for elevating your heart rate. A set of pushups, then squats, then pullups or rows, then glute bridges or hyperextensions, then situps or leg raises (see Alex's blog here)--each following the above pattern of high reps on some days and low reps on others, can form a complete mini-routine that can be done daily. Before too long you'll be hitting some pretty good numbers.
After a few weeks of this (yes, you really will adapt that quickly!) you'll likely have doubled your initial reps, maybe more. I used this format several times when I was just starting out, for bodyweight squats and kettlebell swings. I went from 100 to 200 consecutive squats pretty quickly, and went from under 100 straight swings with a 16kg kettlebell to over 300 straight within less than a month.
The Daily max:
Doing this sort of daily work is extremely effective but after a month or so it can become monotonous for some--that's why I'll have plenty more basic progression examples in blog posts to come. However, if you like the habit of doing 'one set for everything, every day' here's the next step. You'll keep doing one set daily, but stop alternating between 'easy' and harder sessions on purpose. Each day, you'll go for a 'daily max'; this is a maximum effort but not a truly all-out one, something that requires hard work but won't cripple you because you'll be doing another 'daily max' the very next day.
An example with unweighted (bodyweight) squats: your best is 150 reps.
Day 1: 130
Day 2: 120
Day 3: 150
Day 4: 125
Day 5: 140
Day 6: 155
Or maybe something like that. One good way to go about a daily max is simply to do as many consecutive reps as you can without pausing in between. When you're really going all out, stopping and breathing a few times between the last rep (or dozen reps, depending on how many you're doing) is natural. But with daily max work you don't want to prolong the effort. Instead, you'll do close to your best (80-90%, perhaps) without really pushing yourself, every day, and every now and again if you feel good push just a little harder and break through to a new PR. And if you don't succeed in a new PR, don't worry about it--there's always the next day, and the day after that....
This is one of the more effective methods that you can use as a beginner, or for general conditioning, improving your max reps in one set, or building the work capacity to train every day. Try it--good luck!