If you have any questions feel free to PM me. I am an IFA, specialising in this.
Every company is given a date (called a staging date). They can't change that date. Within 3 months of that date they have to automatically enrol certain staff. They are staff aged between 22 and below their state pension age and also earning over £10,000 pa (£833 a month if monthly paid). The others are given the option to join but there is no requirement for company contributions for low earners. Contributions can be based on total earnings between £5824 pa & £43,000 (or can be based on basic or total earnings). Until Apr 18, Employers have to pay in at least 1% and so do you. Then its 2% employer and 3% you. From Apr 19 its 3% employer 5% you. You get tax relief on your contribution. These %ages vary slightly depending on the chosen pensionable salary basis.
IMO Nest is a cheap option which isn't so good. You cannot transfer in or out. Investment options are limited and it is horrifically in debt. But so long as an employer is willing to do the donkey work, its free. Also, in terms of the hours spent sorting it out, it will cost more than alternatives.
You will be written to when the time comes from your employer but can use the weblink if you have your company PAYE Ref. .
To answer your question however, prior to the Pensions Act 2008, employers were legally required to offer staff a pension scheme. They didn't have to automatically enrol staff into it, nor make an employer contribution. Not many employers bothered. Now fines are being made to employers not complying (Swindon Town FC for example) so they have little choice.
PM me if you wish.