How are new bitcoins created without monetary inflation?
Bitcoins are created at a predetermined rate. Until this rate drops to 0 (around the year 2140), the supply of bitcoins is increasing. If this isn't offset by destroyed/lost coins and increased demand, some amount of inflation will occur. However, I'd expect the inflation rate to be low (if positive at all), and getting lower.

Once all ~21 million bitcoins are mined, no more will ever exist, so inflation will cease entirely, and only deflation can occur (again, as bitcoins are lost or intentionally destroyed). There are currently ~12.7 million bitcoins in existence, so at most, inflation will make 1 bitcoin today worth ~1.65 bitcoins in the future.