The part to the art that you think of first (but don't forget about staking if you want to be successful).
This part will vary according to your own interests. Initially, you need to be able to appreciate the relationship between the statistical likelihood of something compared to the odds on offer. This can be purely through feel, through your own pricing, through more sophisticated statistical analysis, or just through receiving tips from other experts.
The Betting Bible Syndicate for example, which focuses on English Premier League Soccer bets, uses a combination of complex statistical analysis, combined with qualitative considerations of team strength.
The syndicate has a panel of bet selectors, including a professional poker player, an ex-professional footballer, and statistics trained professionals. The statistics team use historic results data in order to determine independent prices, and this is then compared to the prices available from bookmakers, along with the qualitative considerations. The combination of the skills of this panel is then used to identify bets place, determine the appropriate stake sizes, and execute bets for the syndicate.
The Betting Bible premier league football bet tips can help give you a further insight into the considerations made to determine value bets.