You can simply type in the domain to start with a first check:
Voila. At the moment of writing google.de resolves to the IP 172.217.16.131.
This is the full output:
Explanation:
<<>> DiG 9.10.6 <<>> : The installed version
opcode: QUERY: The action, dig took.
status: NOERROR: There as no error, it could also have SERVFAIL (Name exists, but data is invalid), NXDOMAIN(Name questioned does not exist) or REFUSED (Nothing is supposed to be served here).
QUESTIONS SECTION: What did dig look for? Default are A records, so it is listed here
ANSWER SECTION: This is the most important part showing the results. It shows that google.de has a TTL of 281 and an A record to the given IP.
Query time: We had 51msec. Out of curiosity you could compare some DNS Resolvers at dnsperf.com
SERVER: This is the server being used, in the given result my local router rechable at the IP 192.xxx.xxx.xxx is my DNS server and therefore answering.
As I wrote, dig outputs A records, you have to explicitly ask for other ones, e.g. you can do:
You can ask for all existing records with ANY:
Using a different DNS server for a request
Sometimes your local computer, browser or router caches DNS entries and you are not able, to see changes for some time. You could change the DNS server in your system or temporarily use another public DNS server, e.g. 8.8.8.8 (Google), 208.67.222.222 (OpenDNS), 1.1.1.1 (Cloudflare).
Checking on DNS Nameservers
Simple check to get the Nameservers:
You can also use +nssearch, to get the IPs and the SOA informations:
It shows the name, admin/owner informations, the SOA record serial, the refresh TTL (from slave -> master), retry TTL (retry time, if initial refresh failed), expiry TTL (time after which the master should be considered gone, if both fail) and NX TTL (How long must a NXDOMAIN result be cached by the resolver), the IP and the query time. You can read further about this here.
Specifiying nameservers or their IPs can help to check, if those resolve correctly:
How can I do a reverse DNS lookup?
Seems like google.de to me is served from Frankfurt and Zürich.
Tracing DNS with dig
This gives us the full trace of DNS name resolving works for google.de. There are 13 root servers, they have info on the TLD authorative servers (NIC is responsibe for .de TLD and they have google.de on file. More about tracing can be found here or here.
BTW: The DNS records DS, NSEC3, RRSIG are part of the DNSSEC protocol. You can find a good explanation of those at Cloudflare. More about root servers, registries and the general structure can be read at the Internet Assigned Numbers Authority (IANA).