heavy soil (clay i presume?) is not all bad. true, it's difficult to dig and sometimes you have clay bricks that just wont break up. but despair not!
i have the very same on my plot. compost or manure will add nutrients, but clay is normally a good soil, holds water well. i hardly watered all summer - the top looks bone dry but one or two inches down it's nice and moist :)
you will have really trouble raking the soil to a fine tilth. i sowed a lot of my really small plants (celery, celeriac, herbs etc) inside in pots, and planted them out when they were big enough and didnt mind being planted amongst huge lumps of clay :)
another trick is to make a line, fill it with compost and sow directly into that. this way you also see exactly where you have sowed and what comes up should be almost 100% weed free. i have done lettuces this way. it also means that the soil/compost above that seed row will be easy to break through for the seedlings - clay soil forms a hard crust under wet-dry conditions which might make it diffuclt for little plants.
carrots and parsnips - i have chosen a small carrot variety - round carrot, that doesnt need to go down very far. for parsnips, i dont grow that many so i station sow them into dibbed holes filled with fine crumbs/compost. again this is to do with helping the seedlings along, and providing a deep stone free area (hence the dibber hole) - i have hardly had any forked 'snips :)
work with what you have. and don't despir. once the plot is underway and the plants are growing, the soil will come into its own! and by the end of the season, it does look very managable and lovely - i covered a lot of my beds with water-permeable plastic so that the soil structure wont get too damamged and compacted over winter (heavy rain etc)
as to your sand question: you can add sand but it wont make your soil better. just a little less claggy. and you would probably need a lot.
lay out some paths between your beds, dont step on the soil and it's as good as it gets, i think
hth
svea