First you need to identify what weeds you've got, which will help you to decide the easiest/most long lasting way to get rid of them. I'm pretty sure that you've got garlic mustard there, which is a perennial and needs either herbicide or to be dug up. Anyway! Take a couple pictures - close ups - of each type of weed and post them in either the Name That Plant forum or the Weeds forum (one plant per post to make it easier).

In the interim, you need to decide if you would use herbicides if they are called for (many people refuse to use them on principle), and what you intend to do with the area when it's clear.

Post soon, so we can get you started!

Herbicides are the fastest and most efficient method of control but not always the most popular method. For most herbaceous weeds (those with no woody stems), smothering is a very effective and non-chemical means of control. Just gather up as much cardboard as you can lay your hands on, layer it on, wet it down, then cover with mulch or soil. By the end of the season you will have smothered all the weeds, the cardboard will have broken down and decomposed and you will be left with a loose, plantable soil.

If you want something faster, you will either need to resort to herbicides or digging the entire area up. That can be a lot of work but is the most effective non-chemical way of dealing with weeds if one is thorough in their approach. And it doesn't really matter what kind of weeds you have.

The taller plants with white flowers are garlic mustard. My condolences on that. It'll be a long time before the seed bed has been exhausted. But keep at it!

what kind of gardening do you hope to do there? possible raised beds might work