We find in Acts:
Acts 2:2-4 (ESV)
"And suddenly there came from heaven a sound like a mighty rushing wind,
and it filled the entire house where they were sitting. And divided
tongues as of fire appeared to them and rested on each one of them. And
they were all filled with the Holy Spirit and began to speak in other
tongues as the Spirit gave them utterance."
In these verses the Holy Spirit (strategically) empowered each of his apostles to speak in other tongues.
From this static experience, we can see 'filling' as a potentially recurring event in a believer's life. Praying for God to 'fill us with Your Holy Spirit,' can be an everyday prayer.
The indwelling, seems to me, appears later in this same chapter as Peter speaks about the 'gift of the Spirit':
"And Peter said to them, "Repent and be baptized every one of you
in the name of Jesus Christ for the forgiveness of your sins,
and you will receive the gift of the Holy Spirit."
Though the word 'indwelling' is not in this passage, the word 'gift' implies that each person will be receiving the Spirit for the first time - the indwelling of Him. Indwelling and the opinion of when it occurs varies from denomination to denomination. According to this passage, when a person repents in faith, they are given the Holy Spirit as a gift, the indwelling.
Here is a launching webpage for some differing doctrines and beliefs on Holy Spirit filling and 'baptism': http://christianity.about.com/od/glossary/g/baptismholyspir.htm