I build trash cans, hire handy men, set patrol areas and it just keeps getting worse.

What am i doing wrong?

For your handymen, make sure they're not allowed to cut grass as one of their jobs, that seems to take up a lot of their time and keeps them from sweeping and emptying trash bins. From a design perspective, you want to minimize the possible paths a handyman can take on the foot paths so they will cover any particular area as much as possible.

You definitely should not assign large areas to a handyman. Make it around 6-10 fields max and it should suffice even when it's crowded.

Complex paths running under or over each other tend to make them stuck somewhere.
Also, try to avoid "snakey" waiting lines. They usually don't need cleaning anyways but I often find Handymen walking back and forth in there without ever coming back out.

Regularly keep an eye on visitor thoughts and check for problem zones on the diagram. Just click on the entry with the "disgusting path" thoughts and then click on the map symbol to see a park map with blinking paths where these people are. Then check on your Handyman that's supposed to patrol there.

You will get more trash on the floor for quite a few reasons. Here are a few pointers to keep in mind while building your park.
-Build gentle rides close to each other and keep them relatively separated from the more extreme rides.
-Build Food/Drink stalls away from more intense rides. If guests get sick just looking at the roller coaster, they are going to puke right after eating.
-Build bathrooms and benches close to the exits of highly intense or extreme rides.
-Build benches on every other square of path you have. Giving guests a chance to sit (especially after climbing or descending an inclined path) will help alleviate their sickness.
-Put lights on your queue line paths. Lights function as a precautionary measure of reducing vandalism, but you don't want them flourishing on your regular foot paths. If you have a particularly long inclined path, you should put some lights on it.

-Hire a lot of handymen. Go to the job checklist tab and uncheck mow the grass. You will even need to do this in scenarios that have no grass otherwise they will search the entire park for grass. Make sure to assign them patrols. For small to medium parks I tend to assign 3-4 patrol areas per handyman. Of course the patrol areas should be adjacent and be covering a foot path. I don't think queue lines ever get dirty, but it might be safe to add the extra 1 patrol area for a queue line just in case.

-If guests are complaining "Its too crowded here" you will likely be spammed with garbage on the floor no matter how many handymen you have. You need to expand the width of your foot paths by 1 or 2 squares. Check to see where guests are complaining about the problem and only fix the footpaths that will make the most difference.
-Making a park too compact will cause this complaint to happen frequently and while it won't hurt to complete a 2 or 3 year objective, you'll want to plan ahead for expanded foot paths in larger, longer lasting parks.
-You will also want to create multiple ways for your guests to leave the park. A crowded park means that it will take guests longer to get out.

-As far as vandalism is concerned, you need to hire security right away and you'll want about 3-4 for a medium sized park. If vandalism persists and guests are complaining, just do a quick fix and replace the broken benches/trash cans/lights as soon as you find them.