The actual act of collecting data can be done by the project workers and/or volunteers. This can include recording attendance at activities or events, conducting surveys and doing interviews.
This data can then be analysed by project workers or service managers and included in reports or fundraising bids. There are no rules here about who does what; it is very much dependent on you and your organisation. It is also possible to commission an external organisation to do the work of monitoring and evaluation.
The work of monitoring and evaluation can be done both internally and externally to the organisation.