There are three ways to do it:
Either...
... the captain sits in on selection and has a direct influence on who is in the team. Captain ends up happy when he has his way. Captain ends up unhappy when his view is clearly not that of the selectors.
... the captain has an influence on the selection, but is not directly involved. IMO this only results in the captain not getting his way.
... the captain has little influence on selection, and just makes the best of the team that turns up.
I think the best method is the last one (provided we are discussing an international side, not a state/county/club side). Should the captain sit in on the meetings, there could be two problems: a) the selectors diagree with him, damaging their relationships, or b) players are unhappy with the captain if they are dropped since he has some direct responsibilty with that player being dropped. Imagine if Dravid had had a big influence on Ganguly being dropped, not necessarily this time, but before Christmas against Sri Lanka? He would have been the scapegoat of the pro-Ganguly gang.
If you use the second method, there must be a healthy trusting relationship between the captain and the selectors. It can work well, but can fall apart easily.
The last method seems to me to be the best. If the captain has a clear conscience about selection issues, then he will remain well respected by his team mates even if poor selections are made - the selectors will be the ones under fire. It allows him to think more about on-field tactics, and to concentrate on his own game. The only problem with this really occurs somewhere like India, where the selectors are heavily biased towards players from their own zone. This is where the captains influence may be helpful, particularly if he has done his job correctly and has a good understanding of the players in the frame and has the team's best interest at heart.
With regards to the Lewis/Peterson situation, I don't see this as a major selection problem involving the captain, what we have here is a) lack of Australian bowling backup, and b) lack of a South African spinner. If the captain has a serious problem, then he should make his views clear to the board, but if these players are deemed to be the best possible by the selectors, then it is difficult to complain.
Actually I have been more impressed by Peterson than I have been by Boje in the past. Admittedly I have only seen him bowl recently in the Pro20 and Sunday's ODI, but he looks capable of turning the ball and getting out batsmen, whereas Boje never looked like taking more than a couple of wickets a match.