Downloading the CSS and re-uploading it as a static resource is unnecessary. You can use the SLDS stylesheets by adding the <apex:slds /> tag to your Visualforce page. This is documented on the SLDS site under Visualforce, the download is offered if you want to use the CSS outside of Salesforce.
You can also scope where you want the SLDS styles to be applied.
<apex:page standardController="Account" applyBodyTag="false">
<apex:slds />
<!-- any Visualforce component should be outside SLDS scoping element -->
<apex:outputField value="{!Account.OwnerId}" />
<div class="slds-scope">
<!-- SLDS markup here -->
</div>
</apex:page>
Additionally, make sure you're using the appropriate markup for the SLDS class names. Many of the classes that use double hyphens (--) have been deprecated.