You typically have two kinds of IDS, network-based and host-based, and these can be signature or statistical response types.
Signature IDS's are simple, fast, and can be updated easily. Usually vendors supply signature files - similar to the way anti-virus vendors supply virus signatures. For this reason most IDS's use signature recognition. The downside is that they will not identify a new attack unless it has a signature which matches an existing attack.
Statistical or heuristic IDS's learn what 'good' or normal traffic looks like and alert on anything which isn't normal. This does mean they are much better at spotting new attacks, but does require learning periods when initially installed and regularly on the implementation of new servers, services and when any new traffic types or volumes are expected.
Network based IDS's are usually implemented at the [erimeter of an organisation, and they have visibility of all traffic entering (and sometimes exiting) the organisation. Where traffic has indications that it may be malicious it is logged or flagged to a response system or person.
For a large organisation, the amount of different valid traffic types can be very high, and the traffic types can vary over time so the ongoing configuration and tuning of a perimeter network based IDS can take a lot of resource. For this reason, the majority of large companies outsource this to vendors who provide the service to many organisations. These vendors have better visibility of attacks happening, a scale advantage on tuning and response, and the ability to update signatures for all their clients at once.
Host based IDS's are more usually implemented in-house for specific high-value servers. The traffic types and load are usually much lower and more predictable so the resource requirement is usually lower.
Also have a look at this question - some discussion on anomaly based (statistical) IDS.