Here are some ideas:
Make your list sound interesting. Signing up to a newsletter sounds dull, but joining a gang, a party or a fan club may sound more appealing. Have fun with the name and use your brand voice fully.
Give them a reason to sign up. It's not a one way street and it's not about you selling or sharing your news. It's about adding value and giving your audience something special. Perhaps they get exclusive content or links to your products ahead of others. Maybe they are all VIPs in there? Make them feel special.
Try using a landing page. This is a website style page that you can use to invite people to opt into your list - perhaps with a reward. This can be linked into your social posts to make the sign up process more attractive and fun.
Integrate your sign up forms with your social and website. Add sign up forms to your website or even pop ups. These can be designed and the code added very easily and for free. Also integrate your sign up into your Facebook page (Mailchimp integration is free) and perhaps into your Instagram bio too.
Offer a thank you gift. To emphasise the special nature of your list, offer a thank you like a discount code, free checklist, recipe, intro video, pattern or inspiration board. These can be set to go out automatically as part of your automated 'welcome' email that you set up in Mailchimp or other platform.
Use your list like a waiting list. If you are closed or building to a launch, invite people into your list and let them know that they will hear 24hrs ahead of anyone else.
Invite your subscribers to invite their friends. Make sure your content is valuable and remind your readers that if they invite a friend, that their friend will also get the thank you gift. This can be done by using the 'social share' feature in most email marketing platforms when used within an email.
Add your sign up link to your email signature, receipts, invoices or thank you notes. All email marketing platforms offer a free link to your sign up forms.