As most jobs are advertised online, do consider enrolling in a basic computer course if you are not familiar with using the internet to do research.
Good places to start are employment agency websites - research those that specialise in your field or the kind of work you are looking for, including temporary work.
Look at the online versions of national, local and trade press too as fewer jobs are advertised in print these days.
Check out the job pages of organisations and companies you are interested in and set up job alerts to receive email message when suitable vacancies arise.
Jobcentre Plus may be able to help pay for replacement care while you attend appointments, interviews or take part in training arranged by them. Call 0345 6060 234 to find out more or go to https://www.gov.uk/moving-from-benefits-to-work/help-for-parents-and-carers
Networking - tell friends, neighbours and former colleagues that you are looking for work and join online communities such as www.uk.linkedin.com to let others know you are in the market for a job.