Salesforce Lightning Design System(SLDS) classes can be used to align lightning-button in Salesforce Lightning Web Component.

Sample Code:

Lightning Web Component HTML:

<template>
    <div class="slds-clearfix">
        <div class="slds-float_left">
            <lightning-button 
				label="Left" 
				class="slds-m-left_x-small">
			</lightning-button>
        </div>
    </div>
    <div class="slds-clearfix">
        <div class="slds-align_absolute-center">
            <lightning-button 
				label="Center" 
				class="slds-m-left_x-small">
			</lightning-button>
        </div>
    </div>
    <div class="slds-clearfix">
        <div class="slds-float_right">
            <lightning-button 
				label="Right" 
				class="slds-m-left_x-small">
			</lightning-button>
        </div>
    </div>
</template>

Output:

We can also make use of lightning-card footer slot to place the lightning-button in the bottom center.

Sample Code:

Lightning Web Component HTML:

<template>
	<lightning-card  title="Example">		
		<p class="slds-p-horizontal_small">
			Testing Content
		</p>
		<p slot="footer">
			<lightning-button 
				label="New"
				variant="brand">
			</lightning-button>
		</p>
	</lightning-card>
</template>

Output: