Mongodb high lock percentage / slow queries

I'm working with an application using MongoDB that is getting a fairly large number of incoming requests and I've noticed that the responses are getting slower as the number of requests get higher.

I'm suspecting that there is some inefficiency with the database. I ran mongostat during one of our higher load periods and the result seems to indicate high lock percentage:

insert  query update delete getmore command flushes mapped  vsize    res faults           locked db idx miss %     qr|qw   ar|aw  netIn netOut  conn set repl       time
*0   1120    479     *0     179   472|0       0  72.1g   146g  1.31g      0 server-prod:15.7%          0       0|0     1|0     1m     4m   298 rs0  PRI   15:37:28
*0   1192    509     *0     178   428|0       0  72.1g   146g   1.3g      0 server-prod:18.9%          0       0|0     0|0     1m     5m   298 rs0  PRI   15:37:29
*0   1107    456     *0     174   362|0       0  72.1g   146g   1.3g      0 server-prod:20.4%          0       0|0     2|1     1m     5m   298 rs0  PRI   15:37:30
*0   1320    556     *0     211   532|0       0  72.1g   146g   1.3g      0 server-prod:19.5%          0       0|0     0|1     1m     6m   298 rs0  PRI   15:37:31
*0   1094    474     *0     179   449|0       0  72.1g   146g   1.3g      0 server-prod:15.7%          0       0|0     0|0     1m     5m   298 rs0  PRI   15:37:32
*0   1120    487     *0     184   458|0       0  72.1g   146g   1.3g      0 server-prod:20.8%          0       0|0     1|1     1m     5m   298 rs0  PRI   15:37:33
*0    807    299     *0     108   270|0       0  72.1g   146g   1.3g      0 server-prod:15.3%          0     103|1     0|3     1m     3m   298 rs0  PRI   15:37:34
*0   1613    709     *0     161   146|0       0  72.1g   146g   1.3g      0 server-prod:63.5%          0       0|0     1|0     2m     7m   298 rs0  PRI   15:37:35
*0   1133    472     *0     167   341|0       0  72.1g   146g  1.31g      0 server-prod:21.2%          0       1|0     0|1     1m     6m   298 rs0  PRI   15:37:36
*0   1292    555     *0     189   440|0       0  72.1g   146g  1.31g      0 server-prod:23.3%          0       5|0     1|4     2m     6m   298 rs0  PRI   15:37:37

The 3rd line from the bottom has a lock percentage of 60% which is pretty crazy considering the average lock percentage is around ~20%. On higher loads the average goes up to 35-40%.

I also ran show log in my production mongo shell and have not seen a single query that ran below 100ms. Some of the queries have an execution time of ~700ms to 1s.

The machine the database is running on might also be the problem (an n1-standard-1 (1 vCPU, 3.8 GB memory) google compute engine VM instance).
The database is also structured as a three-member replica set (one primary and two secondaries with no arbiter).

What are some ways I can troubleshoot and increase my query speed?

Thanks!

EDIT: Forgot to mention that I'm using Mongo v2.6

EDIT: Here is the output of db.stats()

{
"db" : "server-prod",
"collections" : 20,
"objects" : 36560,
"avgObjSize" : 359.20568927789935,
"dataSize" : 13132560,
"storageSize" : 43479040,
"numExtents" : 62,
"indexes" : 24,
"indexSize" : 6189232,
"fileSize" : 67108864,
"nsSizeMB" : 16,
"dataFileVersion" : {
    "major" : 4,
    "minor" : 5
},
"extentFreeList" : {
    "num" : 0,
    "totalSize" : 0
},
"ok" : 1

}

EDIT: Last night I saw my CPU go up to 128% during peak load hours, how is this possible? (This is a single core machine)

EDIT: I created indexes on some of the most queried fields and noticed an increase in performance, however, the update queries are still taking way too long (~500-800ms). What are some optimisations I can do to increase update/insert performance?