WooCommerce Multistep checkout plugin is based on the JavaScript, so if there are javascript errors on your checkout page then checkout wizard will not work.
There could be several possible reasons of javascript errors on your checkout page. For example you have included jQuery multiple times or another plugin is generating javascript error.
As soon as you are able to fix those errors WooCommerce Multistep checkout plugin will begin to work.
Go to "Woocommerce => Settings => Accounts" and check "Display returning customer login reminder on the "Checkout" page " option
Plugin provides number of hooks to add extra step in the wizard. Please go to Plugin Documentation and see the examples and available hooks.
Some time date picker added by third party plugins does not work in the WooCommerce MultiStep Chekcout Wizard. In order to fix this issue you need to to plugin setting of this plugin and see the very last option Code Location. Try chaning the value from footer to header.
In order to combing Billing and Shipping tab, go to plugin settings and set Combine Billing & shipping to "yes"
Add following CSS into your theme style.css
.woocommerce form .form-row-first,
.woocommerce form .form-row-last,
.woocommerce-page form .form-row-first,
.woocommerce-page form .form-row-last {
float: left;
width: 47%;
overflow: visible
}
.woocommerce form .form-row-last,
.woocommerce-page form .form-row-last {
float: right
}
.wizard .input-text, .wizard input[type='text'], .wizard textarea, .wizard select {
width: 100%;
box-sizing: border-box;
}