I'm going to assume that you are knitting on 2 straight needles, and that you are knitting stockinette.....this is done by knitting on one side, and purling on the other, which together create stockinette. For stockinette stitch, you ALWAYS knit on the right side, and purl on the wrong. Thus, when you pick up your knitting and get ready for the next row, if the right side is facing you, you knit....if the wrong side is facing you, you pearl.
There should be a piece of yarn left, when you finish your cast on.....when you finish your project, you can either weave it in with a croched hook, or thread it on a blunt tipped plastic needle with a very large eye (made for yarn), and use this to weave it in place. It's okay to cut some of it off, in the beginning, if it's extremely long, but don't cut it off short....you need plenty to work through, to keep it in place. If you're making a scarf you might want to add fringe to the ends and if so, you can incorporate that left over piece into the fringe.
Are you using some sort of a different edge to your scarf...by that I mean on the first few stitches on each row? or are you just knitting across and then pearling back? If the latter, I'd suggest that you knit the first and last 4 stitches on EACH row...that means , on the pearl rows, you knit the first 4 stitches, then pearl across till you get are left with 4 stitches on your needle....and then knit the last 4 stitches. Plain stockinette edges will roll up, but if you put a garter stitch edge on the sides (garter stitch is done by simply knitting both sides) it'll makes a pretty way to keep the sides from curling. You can also knit a scarf in all garter stitch...that is, knitting both sides....pretty and no need to do anything different to keep it from curling - garter stitch will take care of the problem.
Have fun....that's what it's all about!!!

Look at where the bumps are. A purl stitch puts the strand of wool towards the front making a small bump. A knit stitch puts it at the back. That is why when you do stockingette stitch--knit one row, purl one row-- the front is smooth and the back is bumpy.

You always have a length of yarn at the end when you cast on. If it is too long you can clip it agter a few rows, but keep enough to darn in. Yes it must be darned in. I prefer to use a wool bodkin--darning needle without the sharp point, but you could use a crochet hook. Don't pull it too tight and go back and forth a bit. Those tails come in handy for sewing seams of sweaters and such when you graduate to them

I use the tail as a marker ;0) When you've finished casting on, you will turn the project around and the tail should be on the right side I usually knit across the first row and then purl back, so if the tail is on the right I know I should knit, if the tail is on the left then I should purl...after a while you will know which is which by the shape of the stitches. HTH ;o)

If none of the above make sense yet (as you're too new of a knitter..)...get some kind of "stitch marker"...a, different colored yarn, you don't have to buy stitch markers, though they are sold. Make one RED (Right side)...and one Blue or something...(WRONG side--Oh Purple...for PURL side)..and place it on your knitting, so when you look at that side of the knitting you know you're on the Right side and have to KNIT or the Wrong (Purl) side and have to Purl. After a while you'll start to recognise the knit and Purl stitch and not have to worry about the markers. That is why I say don't worry about buying some. See Oilpainter's post for which is Knit and which is purl.

If you're more visual, I've attached a link..beest I could find. The purl shows how purling looks, the "increase" and the rest pretty much show knit stitch.

Vickey-MN

Here is a link that might be useful: identifying stitches

What I do is take a safety pin and pin it to the right
side of work (knit side) so I remember which side I am
working on. Hope this helps.

I almost always use the "long tail" cast on method, which leaves the tail of yarn at the "pointy tip" end of the needle. That would be the end to my right as I hold the needle in my left hand to begin knitting. The empty needle will be in my right hand.

Your scarf may have a border at both ends that will be different from the "body" of the scarf. Let's say, for example, that the instructions say to knit 4 rows in garter stitch (knit every stitch for 4 rows).

When you're done with those four rows and you turn the needle to begin the next (5th) row, the yarn should again be on the right-hand (tip) side of the needle.

Often the instructions will then start numbering the rows with Row 1. In other words, the border isn't Rows 1 through 4. The first row of the pattern stitches will be Row 1. The instructions pretty much ALWAYS say whether Row 1 is a Wrong Side (W) row or a Right Side (R) row.

So, now all you have to do is look to see if you're going to be working a W or an R row. You can make a little notation on your written pattern as to which row has the tail on the right-hand side. That is, if the instructions say that the first "pattern row" is the Wrong side, take a pencil and write a "T" (for "tail") next to Row 1 on the pattern.

Whenever you need to figure out whether you're on a Wrong or a Right side row, just look at where the yarn tail is. If it's to your right, it's a Wrong side row, and if it's to your left, it's a Right side row.