There are many ways to delegate Steem Power on Steem blockchain, one of them is with Steemconnect.
Delegating Steem Power
First, decide how much Steem Power you want to delegate and convert it into Vests.
What are Vests?
Steem Power is essentially Steem held in a fund. Vests are Shares in that fund.
Use this calculator to convert Steem Power to Vests.
I want to delegate 900 Steem Power so I will go to site and enter 900 Steem amount in respective field, and it will show up Vests amount.
always calculate Vests before delegation, since Steem to Vests rate flunctuates
Once you get Vests amount, change details in the link given below.
https://steemconnect.com/sign/delegateVestingShares?delegator=youraccount&delegatee=otheraccount&vesting_shares=vestsamount VESTS
Where "youraccount" is delegator — who is delegating Steem power, "otheraccount" is delegatee who is receiving delegation and "vestsamount" is Vests amount (i.e. Steem Power) you are delegating.
I (
https://steemconnect.com/sign/delegateVestingShares?delegator=libert&delegatee=shivohum2015&vesting_shares=1839880.6565 VESTS
(Remember, there is space before VESTS word)
Go to the link and it will show you what you are going to do (Ha!).
Click confirm and enter your active key (or master password but that's not recommended).
Shh...don't look at my password
Click Sign In and you will get congratulations message.
Checking If Delegatee Got Delegation
I have OCD, so you know.
go to https://steemd.com/@yoursteemusername and it will show you the delegation.
For example, https://steemd.com/@libert
Undelegating Steem Power
There is already a very good guide on that by 
Once you undelegate Steem Power there is 7 days cool down period, that means you will have to wait 7 days to get Steem Power back in your account after undelegating it.
If you have doubt or any kind of feedback, let me know in comments!