Go to Wal Mart. You will find several cans/ brands/ types of oven cleaners. It's best to just read the details on each can as all work differently. Some will require you to heat the oven prior to spraying it, some only have to stay on a few hours and some must stay on overnight, some can be used BOTH ways, with better results if left on overnight though. And, some will be fume free and most importantly, so will say "fume free." Even though they SAY fume free, ALL are going to have some fumes, just less than the ones that don't make that claim.
I have found for a very dirty oven, the ones that say they work for BOTH oven and BBQ grills are best, If you don't get that type, you are likely going to have to do it a second time to get a lot of grime off.
Other tips- make sure you do not have a "self clean" feature on your oven. Even self cleaning ovens need a cleaner if they have not been cleaned very often and theirs a lot of soil. If it says that, even if the feature doesn't work, you still must get a cleaner that says it is safe for self cleaning ovens.
Keep the cleaner off the oven light.
Don't let cleaner, or anything w/ the cleaner on it (gloves, rags, etc) come in contact w/ any other surfaces as it will damage those surfaces. VERY important is to put something (old towel, heavy paper towels, etc) between the bottom of the oven door and the drawer under it, as it has a tendency to leak out onto the floor or oven finish on a lot of ovens,
Get a steel wool pad for all of the little brown specks that will likely remain after oven is cleaned if oven is very dirty.
If your oven has a glass door, that can get very dirty quickly and be hard to clean. I buy one oof those $1 paint scraer blades (again Wal Mat paint dept) and use it right before it's time to wipe the cleaner out and also for touch ups of the glass betwen cleanings. So, if you have on your oven light and have company, you don't see those specks or drips of stuff through the galss.
Most oven racks can not be cleaned in the oven w/ the cleaner, you have to take them out. I am guessing since you rent, you do not have the oven manual? If not, play it safe and get the type of oven cleaner I was speaking of that says for both ovens and BBQ grills. I am out and don't recall the name, but it's in a blue can at Wal Mart. It will say, great/ safe for oven racks too. I still take my racks outside and spray them, as even though it's safe to do in the oven, if the oven is very dirty, it's too hard to try and clean it w/ racks in it. Plus, you can easily get all of the residue off w/ a hose.
No matter what kind you get, all will leave some white residue after you have cleaned the oven. It's inevitable that you will miss a spot or two in wiping it down and you won't see it until after you have cleaned oven and it's dry.
Also, after oven is cleaned and before you want to cook in it the first time, turn it on several hours prior as you will still smell some fumes. I do that and then when the oven is just warm, take another damp rag and wipe any tiny spots of cleaner I might have missed.
If like most of us, you have limited time, try putting some foil down on the bottom of the oven floor to catch things that make that part of the oven the first to get dirty. They also make special disposable foil trays (found with foil pans at the grocery) especially for that purpose. Then, when one gets dirty, you just toss and replace. You will still have to clean the oven, but it will be less often and much easier next time.
Last tip- If you don't like the first oven cleaner you buy, try another. It took me YEARS to figure out all I have written above- the best cleaner, easist way to clean both the oven and the racks and ways to make it less of a chore next time.
It's a pain, but you will feel great looking at that sparkling oven....OK, maybe that's an exageration, but you will definitely feel BETTER. LOL