How do you know if the fund is performing well?

This is quite complex and if you don't have a degree in statistics, it might be a little hard to follow but the general idea is to look at the returns, relative to the risk. The following is a list of common measures which gives a clearer picture of the past performance of the fund (from Wikipedia). (There is some contention that this is a poor indicator of future performance.)

Alpha represents the fund's return when the benchmark's return is 0 (0 would be placing it under your mattress as you will not get 0 returns). This shows the funds performance relative to the benchmark and can demonstrate the value added by the fund manager. The higher the 'alpha' the better the manager. Alpha investment strategies tend to favour stock selection methods to achieve growth.

Beta represents an estimate of how much the fund will move if its benchmark moves by 1 unit. This shows the fund's sensitivity to changes in the market. This means how much better is performs compared to the market. If the market is moving down, does the fund also move the same way, or does it move in an opposite way? And how much does it move in that direction? Beta investment strategies tend to favour asset allocation models to achieve out performance.

R-squared is a measure of the association between a fund and its benchmark. Values are between 0 and 1. 1 indicates a perfect correlation and 0 indicates no correlation. This measure is useful in determining if the fund manager is adding value in their investment choices or acting as a closet tracker mirroring the market and making little difference. For example, an index fund will have an R-squared with its benchmark index very close to 1, indicating close to perfect correlation (the index fund's fees and tracking error prevent the correlation from ever equalling 1).

Standard deviation is a measure of volatility of the fund's performance over a period of time. The higher the figure the greater the variability of the fund's performance. High historical volatility may indicate high future volatility, and therefore increased investment risk in a fund.

More details on choosing a fund can be seen on the ASX website