I'm a small time collector - usually buy a box or maybe 2 of a set that interests me. From the box will usually get a full base set, and a bunch of cards from the various chase or parallel sets. How do others go about completing these chase sets (if they even try). Don't feel like buying additional boxes in hopes of getting some cards I need (and then end up with additional base sets that just take up space). Could probably but some complete chase sets on the auction sites, but then I would end up with duplicates of the few chase cards I originally pulled. And I like the feeling of opening packs more than simply buying a complete set. I could look at trading, but then need to decide which sets I want to go after and which I want to give up on. Hopefully I can find some cards I need at the upcoming Philly show.

Card Shows (and other conventions), ebay and trusted friendly card dealers. You pretty much ran the gauntlet there lol

Truth be told, most chase sets or insert sets and even lower level parallel sets can be picked up on eBay pretty cheap. Building in chunks is the way to go.

You need time. I took 5 years off of ebay and did great trading. Now, I ebay a little and trade when I can. If I only had time to get my duplicates in order! Two kids keep me from it!

AWR I know where you are coming from. I try and trade with people because I am always looking to get rid of the extras I have in my collection. If I can't trade then my second tact is going to the shows and buy to fill the holes. I use the 'bay as my last resort.

Unfortunately, eBay is my main source for filling the gaps. I'd very much prefer to trade, but this hobby is far from widespread in Belgium. In Europe in general, actually.
No card shows anywhere in sight. The sci-fi and comic-cons do have the occasional lost dealers, but those are either selling base sets or sealed boxes at premium prices.
So, eBay it is for me.

Being new to this site for just that reason, to try and complete my collections, I tend to use eBay to buy the sealed boxes, then through Facebook, TradeCardsOnline (for most ccg`s), forums and my blog(s) to try and complete either the missing cards or trade off doubles.

But as monkeyafterdark stated above, being in the small country of Belgium where there is next to none `tarde card culture` bar the popular games like Magic, Yu-gi-oh and the likes, it is a pain and often a killer on shipping costs and import duties.

You can sometimes find singles cards on the likes of Ebay.
Or like you said trading.
If you're not buying boxes or full sets there aren't a whole lot of other options aside from the two above.
Unfortunately it isn't like Merlin sticker sets where you [used to?] can write off for the singles you're missing from a set.
Would you be willing to try your luck buying more single packs and hoping you get different to fill in the set?