Either,mow them low,or weed eat them low,then spray with roundup.

If your anti poisons-not a bad way to live- then you can just mow low. If those grasses are like what I get..they are not too hard to pull out by hand really, especially after a good soaking. Some types of grasses are total opposites,you can never get them out if they are near other plants especially. Just keep cutting- eventually they give up. You might find needle nose pliers on those really help.

Some other tools friendly to you and the world are scuffle/hula hoes. I love those. They really can clear out a large area fast and are good exercise!

Nice space! I think most of the dried weeds and shrubs are not going to be very difficult. That ivy (green on the left, maybe covering a small tree?) will be a challenge. Also check the slightly reddish leaves of the viney growth with the ivy--it is very difficult to see in the photos and I am not sure I am seeing it correctly (maybe remaining growth from the support plant through the ivy?), but it looks like it could be some poison oak. Might be nothing to worry about, but I really would not want to read about the consequences if you make an id mistake the other way. :)Congratulations on your new apartment.

Thank you! I'm hoping it's not poison oak. There are tons of blackberry vines that are red....

It looks like those vines are covering a tree with dark brown seed pod looking things. And the tree slightly looks dead. We'll see how many dead trees I can get my landlord to remove!