The nameservers for AstaHost hosting are ns.computinghost.com and ns2.computinghost.com. There are IP equivalents but I doubt it's worth the hassle of going to find them, as I've never had a problem with the two above. What you need to do next depends on if the domain name is for your main site (i.e. the one given in the cPanel) or as an addon. As you say you've got your account set up properly I would assume the latter, but the fact that you plan on hosting the site here without mention of any other sites you have it may also be the former.
If it's your first domain (namely what you specified when you applied to the hosting) I honestly can't remember when you need to point your domain over. If an addon domain then there's a nice little option in the cPanel for adding it. Just fill in the information it asks for and it should be fine. One point to note is that it can take up to a few days for your domain name to point to the new place (i.e. AstaHost), so if it didn't work the first time it may be worth trying again now.
Just a few tips, how useful they are I can't say.
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