Here is a left handed tutorial. http://www.purlbee.com/rotary-cutter-tutorial/

Less expensive left handed rotary cutters here: http://www.quiltbug.com/notions/rotary-cutters.htm

You might want to invest in an Accuquilt Go! die cutter. This is a really good home system for people who have difficulty making accurate cuts with a rotary cutter.

A much cheaper thing to try out first (for straight strips) would be a June Tailor Shape Cut mat. This is a flexible mat with cut-outs to hold your rotary cutter in place as you roll. If your problem is with how you are holding the rotary cutter (the blade should not be tilted as you roll), it will show up when you use this mat.

Altho not left handed, most people try placing their cutter down then cutting. My teacher taught me to place cutter, start cutting then cut into fabric. Come in at an angle. If you place too much pressure on the ruler, you will move it out of place. sut.
Of course you have to have your selvadges matched up and your fabric squared before you start cutting.

Another thought: have you ever tried to cut right handed? It may work.

Another frequent error is having your cutting table height either too low or too high-- either will tend to make your cuts poor.

RST

OMG! I thought it was just me! Lefty too and sometimes my cuts are really wonky and frustrating as all get out! Thanks for the sigh of relief - I will be checking out these links this evening. Thank you all!

When I took my beginning quilting class, the instructor probably spent close to half an hour talking about cutting, Proper ruler placement, how to hold the ruler and walk your hand up to follow the cut, how to hold the cutter, actually making the cut etc.
So you can see that there is a bit to it. I agree with going to your LQS, or a quilting friend to get some pointers.
You make a comment about the lines on your mat. Normally you don't use these lines for measuring or cutting, just rough estimates.

Duh. I didn't realize I could switch the blade. I did, and it already made a world of difference. I do have some problem with the ruler sliding on me, and have looked for some of those strips to make it non slippery, but couldn't find them. Thanks for the help. I will watch the tutorial, too, and practice, practice, practice,....but already, this is easier.

[quote=GrannieAnnie]Mu rulers don't behave, because my lines all run amok.

I went to Lowe's and got a pkg of clear bumps. They stick to bottom of ruler and really help hold them in place.
Also, I use a ruler to find where I want to cut, place another ruler against it, move the first ruler and then cut. I think that means I measure to right of ruler, but cut to left of other ruler. I am right handed, but since using two rulers I get straight lines. Maybe some of us need to measure on one side & cut on the other. I think we all have to find what works for us individually. I cannot fold fabric more than once or I get the wonky angle at the fold.

I also have trouble with the dreaded V on the fold most of the time. If I take the time to find the straight of grain by ripping WOF and then line up the selvages; I usually do all right. Some fabrics seem to be too warped no matter what and then I just cut parallel to the selvages instead of WOF.

To keep the ruler from sliding I have put sand paper dots on my small 6.5" square ruler that I use when squaring up patches or fussy cutting. When cutting WOF, I use my 6 x 24" ruler and keep my pinky & ring fingers on the matt to steady the ruler & slide my hand up it if necessary; pausing with the rotary cutter while I slide.

I keep looking at the June Tailor Shape Cut Plus ruler and daydreaming but I have the Alto Quilt Cut and need to make more use out of it. It will hold the cutting guide & fabric steady but I normally only use it for cutting scraps into usable sizes. I got in the habit of that even though I know it will work for yardage and just haven't forced myself to do it.

Others seem to like using the suction cup handle things on their rulers. There is a thread on this board about finding them at Harbor Freight for much less than the quilt shops charge.