Budget? Positions? You're going to need to be more specific.
I usually just use the search feature, especially under transfer list/expired contracts. This'll be your best bet.
Anyways, young and cheap you could try out Gale Agbossomounde. I bought him in 2011 and loaned him out for the season, and even though he did really poorly, in 2012-2013 he won the starting job and finished runner up for the CB of the year in the Portugese league. Milan Badelj is a great young player who is usually cheap. I got Chico (the Spaniard, from Almeria I think) for like 325k (in dollars) once and he is a very solid CB. Fabio Coentrao is a good winger whom I've gotten for cheap before. But every game is different and will have a different set of cheap, good players. Look for unhappy players and transfer-listed players, or players from smaller leagues who are in the last year of their contract and unsettle them.
If you're looking for quality young players, just look at the threads here. Normally someone writes their team name, budget, position they're looking for, and year, and a bunch of people will write great suggestions. If you look at those threads you'll get a whole list of the best young players for each position.