Most plug-ins are designed to run within a host program such as an audio editor or other music production software, and cannot be run as standalone programs.
Multiple effects plug-ins can normally be run simultaneously by a host program, and most plug-ins support multiple instantiations (the same plug-in being used on more than one track with different settings) - the limiting factor is usually only the speed of the computer.
Plug-ins communicate with their host programs by utilising one or more software interfaces conforming to standards created by the host software developers. Amongst the most well-known companies, Steinberg invented the VST (Virtual Studio Technology) interface for use in its line of products such as Nuendo and Cubase, whereas Apple came up with the AU (Audio Units) format, and Digidesign use both RTAS and TDM depending on whether the processing is being done by the computers CPU, or by DSP chips on one of their interface cards. Make sure that any plug-in you buy supports the correct format, as some products are not cross-platform compatible.
The scalable nature of plug-ins can demand a great deal from your DAW - if youre planning on running many plug-ins simultaneously, you may want to consider taking the load off your processor by adding a DSP (Digital Signal Processing) device. Connected via FireWire, USB or fitted internally in a PCI slot, a DSP card uses its own processing power to take the strain off your CPU, and also frees up RAM. Most DSP devices are manufactured by plug-in producers - the TC Electronic Powercore and Universal Audio UAD-1 for example - and as such often come bundled with several plug-ins. Be aware though that DSP cards all use proprietary formats, and so can only use plug-ins that have been specially written for them, rather than for some of the more common standards mentioned above.
Although some plug-ins offer frighteningly accurate representations of their hardware relatives, for the purist there will always be slight sonic differences which means that plug-ins are unlikely to completely replace their hardware relatives in the near future. Interestingly, the release of a new plug-in reproduction, often causes a revival of the old classic, and in some cases the original hardware versions have even gone back into production.