I have been trying to understand the mechanism of static routing. I connected two of 2621XM routers forming their networks on different subnets but unfortunately even though I am doing static routing commands properly the connection is not being established for some reason. I am pinging PC1 with router 2 but its not working. Is says timed out. Network 1 is 192.168.10.0/25 which is left side of router 1. Network 2 is 192.168.10.0/29 which is on right of router 2.
Use the CLI to configure both routers. There's no sens and value in configuring the settings via the Packet Tracer GUI. If you have an IOS image file go for gns3.
From my experience the problem with people learning static routing is that they forget that routing is a two way process. Router 1 will need to have a static route for the 192.168.10.0/29 network and R2 will need to have static routing for the 192.168.10.0/25 network. Configuring the routers you can specify either the Next hop IP address or the outgoing interface. In case of multiaccess networks like Ethernet it's not recommended to specify the outgoing interface because this will create a directly connected static route, so the router will try to ARP ALL destination devices. It can cause performance issue and if ARP proxy is disabled on R2 all ARP requests coming from R1 will fail. So in your type of configuration you could go for either the next hop ip or outgoing interface.
Like everybody else said, we need to see your configs. But the obvious thing I see is that your two subnets overlap. Network 2 (192.168.10.0/29) is part of Network 1 (192.168.10.0/25). So even if you attempt to ping something in Network 1 that is not part of Network 2 (something in the range of 192.168.10.9-192.168.10.127), the return traffic from Network 1 to Network 2 will never reach Network 2, as Network 1 believes Network 2 (192.168.10.0/29) is part of its directly attached network (192.168.10.0/25).
First, validate that you can ping from one router to the other. If you can't, the link between them is not up/up. If you can, the link between them is up/up.
Once you've got the link between the routers working, you need to apply IP addressing to the endpoints (not the switches). Typically this is automated using DHCP which can be configured in the routers. Endpoints get an IP address, subnet mask, and default gateway (and usually DNS servers).
All you need in terms of routing on the default gateways is a static route on each one, telling it the LAN facing subnet which is accessible across the router-to-router link.