So, I am going to put in our first garden since we moved to this house. Having been reading up on permaculture, I recognize that rototilling is not really the best thing to do. However, where I want to place the garden is all grass. So, should I plant in the ground as it is and mulch heavy to kill the grass?

I'm new too, but we have the same issues. In one of the areas, I'm sheet mulching (basically using the bombproof sheet mulching technique in Gaia's Garden). For my raised veggie beds I'm actually digging them down a bit because I'm going to do some hugulkultur, so I'm digging out the grass, though I'll likely put it all back in at the bottom once I've dug it out. The last place I am planting fruit trees, and I don't think I'll have time this year to do much, so I'm just going to plant a bunch of cover crops and next year (or when I get around to it) I can chop them down and sheet mulch there too.

Cutting the grass very close to the ground will enable pioneer plants to get a foot hold and out compete the grass, but it is a slow process - an excellent resource book is "Design and maintain your edible landscape" by Robert Kourik

I have very mixed views on "roto-tilling".  It is something you do not want to do frequently ("Steel is the death of soil"), yet can be a very useful tool to start a garden.  To prepare "virgin" soil for a plot can take several years using 'no-till' methods.  Roto-tilling can give you positive results the next season.  If everybody went the 'no-till' method, over half would just plain give up before they saw any real results.  Roto-tilling can do in an afternoon what it would otherwise take years to accomplish.  Once you have built good tilth, a simple hoe is all you need.  Use your tool to break up hard ground.  Add a lot of organic mater on top, and use your tool to mix it with the soil.  Plant your crops and watch them grow!  At seasons end roto-till the residue back into the soil and plant cover crops.  In the spring, mow down your cover crops and till them in.  Unless you plan on creating more plots, put your rototiller on Craig's List and sell it: you won't need it any more.

I agree with RustysDog. Gras even though it often seems fragile and hard to maintain is a pain in the ass to get rid of. You don't have to buy a rototiller for two time use. Just rent one.

I depends on the grass. Is it Bermuda? Now is a good time to learn what you're dealing with.

I agree with rustydog,  tilling up the grass for a new plot makes sense.  I personally like the double digging way of starting out strong.  The Irish call that the " Lazy Mans Garden "  its alot of work to start,  but then you are done.  It loosens the soil deep down allowing the plant roots to run deep for water.  Tomatos and pepper roots will go 3 feet or more if they can. If you are digging the dirt that deep adding organic matter of grass, leaves, logs, sticks etc for the hugal kulture thing makes alot of sense to me.  Then the sheet mulch on top and just continue to mulch,  you don't need to till every year.  When I double dig and add organic matter deep down I add some crushed lime to sweeten the soil as I back fill the hole.  Bottom line is that you have alot of options and if you don't like to till or double dig because of the extra work you can use the sheet mulch idea to  kill the grass.  Just make sure that you make it thick enough to kill the grass.  Good luck with your new garden,  I am sure that you will enjoy it . 

PS  If you have never gardened befor you might want to start out small untill you see how much work it is and how much you enjoy growing your own food. 

For really thick and persistent grass I'd suggest covering it with a couple overlapping layers of nice large solid pieces of corrugated cardboard. Two or three layers would be nice but it's up to you how hard you want to tackle it.
Make sure it's closely arranged and overlapped and held down with maybe cinder blocks or something else heavy to keep it in place.

The goal is not necessarily to have it break down, just to be something nice and thick to deprive the grass of fresh air and sunlight, as well as thick enough that the grass doesn't just grow right through it.

I suppose you could use a few tarps as well but I don't know if they'd block light as well as cardboard. Some folks use old carpet too but if it's not thick enough the grass can easily just grow right through the carpet so if you try that, make sure you have some nice thick layering.

Last spring we did the corrugated cardboard box, pizza box and newspaper thing over the grass and lasagna style topping of topsoil, straw and composted cow manure, then added mulch over that.  We created a raised bed of about 8-10 inches.  During the growing season we fertilized with fish emulsion and also added kelp and bloodmeal and some lime.  We had tomato plants over 7 foot tall and they produced like crazy.  Two things that didn't work well were peppers and zucchini.  Powdery mildew on the squash, most likely from over watering.  The green beans did very well.

The cardboard started to breakdown about the end of summer, and the soil was much improved below the beds.  This year we are hoping for better results.  In the fall we added alfalfa pellets, bone meal and coffee grounds topped with leaf mold and some compost.  I have compost in a tumble that has been working since the fall and should be ready in time for the spring planting.

Overall, the cardboard worked well in keeping the grass and weeds to almost nothing.  The mulch used on top was Sweet Peet.   It is a recycled and composted horse bedding that works really well and breaks down within a year.

I hope you have as good a garden as we've had.  We had not had a garden in about 15 years and this worked out so well we are devoting more space this year.  Can't eat a lawn.

I prefer to do a sheet mulch to kill grass and start a new garden bed. However, sourcing enough material for sheet mulching is time consuming, and you might only be able to get enough to do a portion of the space you want, instead of the whole space.

Roto tilling isn't great for the soil microbes, but if you're starting new beds on grass that may have been chemically fried before you got the land, and you only do it to establish beds, it can be a useful tool. Rejecting the use of a roto tiller when establishing beds can be a case of the best getting in the way of the good enough- yes, it's best if you can get enough cardboard, organic manure, organic straw, and mulch to build your beds that way, but sometimes it's not an option.

I'm having a heck of a time sourcing enough organic manure without persistent herbicides in them to build up my beds. I'd rather do deep mulch, but a shallow pass with a rototiller followed by a good mix of cover crops followed by green manure plants followed by high-quality mulch as I can get it, is going to get me to where I want to be a lot faster than insisting that everything have to be OMG PERFECT PERMACULTURE ZOMGS! before I get anything done.

Progress is the key, don't get caught up in doing everything perfectly. If you need to till to get the beds started, just understand why it's not a good thing to till every year, and why getting away from tilling is your best option in the long run.