If that's enough for you, you can stop reading now. For the rest, I'm going to risk over-complicating this with a plethora of extra words and pictures, so here goes...
When you finish a round, you'll have worked into the last stitch before the marker. When you start the next round, the next stitch you need to work into is the one with the marker in it. If this isn't the case, either the pattern is wrong, or your counting has been incorrect, so rip back a round and try again.
The stitch with the marker in is “stitch 1”, and it's the first stitch in the round. I always count from the marked stitch, and of course you must count this stitch into your total: it's a stitch, right?
Let's have an example with pictures.
I'm going to crochet this bit of a pattern:
1) Magic loop, 6 dc. 
2) inc, 6 times. 
Note that this is a UK dc (double crochet), which is the same as a US sc (single crochet). The abbreviation "inc" means increase: make two dc into one stitch on the round below.
You can click on these images to make them larger. I've provided two images of each step: one bare, and one annotated to label the stitches. This is so you can compare and contrast; I didn't want my scribbles to obscure the view of the yarn.
If you're a beginner and have trouble determining what is a stitch and what's a random loop of yarn for the purposes of counting stitches or working into the row below, I have three recommendations:
- The best option is have someone sit next to you and tell you if you're working into a proper stitch or not each time. But this might not be an option for you (it wasn't for me, except on special occasions when my mother-in-law visited).
- As you make every stitch, stick a safety pin through every stitch it as it's formed. It's easy to see a stitch as you've just made it, but harder to see it when you come back to it later. Yes, your work will look like a mess of pins, and you'll need a lot of pins to do this. You also need a "special pin" to show which is the start of the round. Nevertheless, on the next round, you know you will only be working into stitches with a pin in. Pretty soon, the moving all the pins starts to become more annoying than helpful: this is when you know you've cracked it!
- Study these images carefully and compare them to the work in your own hands.
In the next image, I'm about to start round 2. The first stitch I need to crochet into is the previous "stitch 1", so I've temporarily removed my safety pin while I do this. I've inserted the hook under both strands of the little "v".
In the next image, I'm still part-way through the first dc stitch of round 2. I've pulled a loop of yarn through the old "stitch 1", so I have two loops on my hook. The next thing I'll do is pull the yarn through both these loops to complete my stitch. You can see my hook and yarn are poised to do this. Hold on to your seats!
I've finished the first dc in round 2, and it's labelled "new 1". It's the first stitch in this new round, and so of course I'll need to mark it appropriately in a moment. In this round I'm actually making 6 increases, which means making two dcs into each of the six stitches on the last round.
Not much has changed since the last photograph: I just replaced my safety pin into the stitch I just made; it's the first stitch of round 2. Momentarily, I'll need to make another dc into the same stitch, and then two dcs into each of the other stitches labelled "2"..."6" in the image below.
Here's my work at the end of round 2. There are now 12 stitches around the outside of my work. There are no more stitches on the round below left to work into; the next stitch to work will be the one labelled "1". This is the first stitch I'll work into when I start round 3. Of course, I'll need to take the pin out to do this, and then I'll be putting the pin back into the first stitch I make.
You just move the stitch marker up each round: when you get to the marker, take it out of the stitch it’s in, make that stitch, and place it into the stitch you just made.