In brief, a trading strategy is a plan designed to achieve the "best" profitable return(s) using e.g. long/short trades. However, a large proportion of this plan (approximately 80%) will typically involve macroeconomics enabling proactive trading that will improve success rates and productivity way beyond that of reactive directional trading.
Many traders use technical trading indicators to help identify various conditions on the chart. Hundreds of indicators are available on most trading platforms but their predictive performance should first be measured (typically using probability theory) to understand what you can realistically expect. Over time a trader may require an indicator to be transferred to other platforms, if the new platform uses a different language then the orginal indicator code will need to be re-written in that language.
API's empower trading development with speed, scale, insight, and agility. APIs (and derived add-ins) are extremely useful for trading development and allow faster, more reliable, development of trading programs that can take advantage of high-speed order routing and broad market depth.
In many cases a significant financial investment should be preceeded by a prototype. This can first prove that the concept works (proof of concept) before the main investment is committed whilst outlining the optimal structure to achieve it. There are many good commercial tools out there including the languages of platforms such as TradeStation, eSignal, NinjaTrader, Metatrader etc. and last but not least Microsoft Excel/VBA.
Statistical Analysis supports our judgement with logic and help us define e.g. the norm and variations of trading performance to give us an edge. Alternatively Data Mining algorithms build patterns. Two very different methods that can be a very rewarding if used correctly and of course, once developed, can be re-used many times.
Computational Finance lies somewhere between mathematical finance and numerical methods. A branch of computer science that deals with problems of practical interest in finance. Algorithmic trading is a typical application involving trading systems that are heavily reliant on mathematical formulas.