I assume that you need rules for the ICMP (not IP) traffic to allow ping.
First of all, you question could be duplicated to this one: How do you allow ICMP Echo Requests on a Cisco ASA 55xx Router?
However, I use slightly another configuration to allow ping. From your question, I'm not sure on which interface you need to allow it, so I'll just post my configuration as example, please fix it according to your setup:
access-list allow_ping_outside extended permit icmp any interface outside
access-list outside_access_in extended permit icmp any interface outside
access-list allow_ping extended permit icmp any any
icmp unreachable rate-limit 1 burst-size 1
icmp permit any inside
icmp permit any outside
icmp permit any unreachable outside
icmp permit any echo outside
icmp permit any echo-reply outside
icmp permit any time-exceeded outside
Documentation (just google for your version of ASA, e.g. 8.2 or 8.4, there are a lot of official documentation available):
http://www.cisco.com/c/en/us/td/docs/security/asa/asa82/command/reference/cmd_ref/i1.html#wp1697623
http://www.cisco.com/c/en/us/td/docs/security/asa/asa84/configuration/guide/asa_84_cli_config/access_management.html#wp1267985
EDIT: concerning other traffic, it is very hard to guess and I hoped that you could provide more details in your question. I assume that you have 2 active LAN interfaces (with the same security level) and 1 WAN. Then, to allow communication for hosts in different LANs (with the same sec. level), you need to explicitly allow it:
same-security-traffic permit inter-interface
See also: http://www.cisco.com/c/en/us/td/docs/security/asa/asa82/command/reference/cmd_ref/s1.html#wp1421315
If you really use 3 interfaces, please also consider limitations of your license (see number of VLANs):
http://www.cisco.com/c/en/us/td/docs/security/asa/asa91/configuration/general/asa_91_general_config/intro_license.html#55668