Two fold job
1. Lots of organic matter into the soil
2. Topping up the nutrients in the soil
The first and most important thing you want to be doing is making your own compost to incorporate into the soil- rotting down all your garden waste, veg scraps, annual weeds- as all of that will improve soil structure, which is important for good drainage, moisture retention (yes that sounds like a contradiction but you need a balance between the two), soil aeration and to hold any nutrients in the soil structure, including trace elements. Manure does the same thing as compost, but supposedly has higher nutrient content (though i've read conflicting stories on that)
If you havent got plenty of organic matter in the soil then it doesnt matter what you feed the plants- they'll not get the full benefit of it. Organic matter is the nice 'spongey' stuff that gives the texture good soil needs- neither dry and barren or wet and waterlogged.
On top of that, vegetables will benefit from feeding.
As far as I'm aware, compost doesnt have high levels of nutrients to grow "hard", where you're cropping the same patch of land year after year (and taking the nutrients out of the soil in the form of your nice veggies) So you need to replace those.
SOme people use a general purpose fertiliser like Growmore... or you can use chicken pellets, or Fish Blood and Bone- all of which break down at different speeds and have different levels of NPK (nitrogen phosphorous and potassium) - depending on what is growing, as different veg use more of one or the other (fruiting plants like tomatoes and strawberries love potash/potassium, but they still need the other two)
Or you can go up the comfrey tea and nettle tea route which are great food for plants- just rot the comfrey or nettles down to make a liquid feed!? This is a great additional thing to boost the plants, if you have access to loads of nettles or can devote some space to growing comfrey.
Root vegetables dont like recently manured ground- they produce lots of roots instead of the big tap root that you need, so never manure a patch you're about to grow those on
Hope thats of help